the saying that best explains how to integrate a function ∫x^n dx, where x cannot equal -1, by the simple power rule is a) add one to the exponent and divide the expression by the new exponent. b) divide the exponent by 2 c) multiply x by the two and then divide by 3.

the saying that best explains how to integrate a function ∫x^n dx, where x cannot equal -1, by the simple power rule is a) add one to the exponent and divide the expression by the new exponent. b) divide the exponent by 2 c) multiply x by the two and then divide by 3.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 44RE

See similar textbooks

Related questions

Q: A cubical crystal is growing in size. Find the approximate change in the length of a side when the…

Q: SOLVE USING VAREATION Of PARAMETERS OR REDUCTION of ORDER 2 tan'x

Q: | sinh$4x cosh 4x dx can best be evaluated by General Power Formula. A True B False

A: Explanation of the answer is as follows

Q: 3.) Integrate using an appropriate technique: 24100 dx (show all steps) 4x2 + 24x+100

A: We have to evaluate

Q: show how to use integration byparts to find integration (arcsin x)^2 dx

A: Let I=Arcsin x2 This can also be written as: I=sin-1x2 Now if we want to integrate above function we…

Q: The radius of a spherical balloon is increasing at 5cm/sec. How is the volume increasing when the…

A: It is required to find the rate of change of increase on volume of spherical balloon.

Q: A water trough is 7 feet long, and its cross section is an equilateral triangle with sides 2 feet…

Q: alue Theorem to approximate the value of

Q: arccos 2x dx 3.

A: We will use integration by parts. The solution is given below.

Q: 14.Use a substitution to evaluate / aVx+1 dx rVa+1 dx. Show all details of the process.

A: To solve- given integral by substitution method.

Q: A water trough is 8 feet long, and its cross section is an equilateral triangle with sides 2 feet…

A: Given thatLength of water trough is 8 feet and cross section is equilateral triangle with side 2…

Q: csc squared x/2 = 2/1-cosx verify with steps

A: To Verify:

Q: 4) dx (Use integration by substitution.) x' +1

A: As per our guidelines we can answer one question. please repost other Seperately

Q: 3 -dr ¤(x – 2) Integrate:

Q: A light is placed on the ground at a distance of 31 feet from the point at which a javelin will be…

Q: integrate sqrt(x)*sin(x)

A: Let I=∫xsinxdx. To solve this integral, we use the Taylor expansion for sinx and write the above…

Q: A plant grows 1.67 cm in its first week. Each week it grows by 2% more than it did the week before.…

A: It is given that the plant grows 1.67 cm in its first week. Each week the plant grows by 2% more…

Q: Find the indefinite integral. sin(9x) sin(2x) dx (Hint: See the hint for Exercise 50 in Section…

Q: Using suitable method, show that 2 tan" (x+2) dx =- – In 2 .

A: We use integration by parts to find integral tan inverse x.

Q: At a given instant the legs of a right triangle are 16 cm and 12 cm, respectively. The first leg…

A: Given: -The legs of a right triangle are 16cm and 12cm, respectively. The first leg decreases at…

Q: integral sec2(?) tan2(?) d?

A: Given that sec2?tan2?d?To find : Integral Solution :∫sec2?tan2?d?Let, tan?=tsec2?d?=dt∫t2dtt33+c

Q: Give 5 example of Reciprocal rule of Basic Integration Formula.

A: Given: Give examples of the reciprocal rule of the basic integration formula The reciprocal rule for…

Q: Give 5 examples of integration by trigonometric substitution with solution

Q: 2Xin 2. O dy/dx if

Q: A water trough is 8 feet long, and its cross section is an equilateral triangle with sides 4 feet…

A: SOLUTION: Given, a water trough is 8 feet long and its cross-section is an equilateral triangle with…

Q: A river 100 ft wide is flowing north at w feet per second. A dog starts at (100, 0) and swims at vo…

Q: sinh4x cosh 4x dx can best be evaluated by General Power Formula. A True False

Q: Integral of tan^4(x)sec^6(x)dx

A: Sincesec2x=1+tan2xTherefore,

Q: use a geometry formula to find the exact value of the definite interval square root of 16-x2 dx on…

A: The given can be consider as a function,

Q: Bring out the importance of Frii's formula.

A: Answer: For the given data

Q: A water trough is 13 feet long, and its cross section is an equilateral triangle with sides 4 feet…

A: Given: A water trough is 13 feet long, and its cross section is an equilateral triangle with sides…

Q: The base of a right triangle is fixed at 3 ft., the hypotenuse is 5 ft. Iong and subject to change.…

A: Pythagoras Theorem states that in right triangle the length of square of hypotenuse is equal to the…

Q: 5 8. fcscz x cot3 x dx

Q: = tanh (2x) Use the definition of the hyperbolic functions to prove the identity 1– cosh?(2x)

A: 1-1cosh22xUse the Hyperbolic identity: 1coshx=sechx=1-sech22xUse the Hyperbolic identity:…

Q: A plane can fly 820 Km with the uwind in the Same time that it' can fly 620 Km against the wind. The…

A: We have to find the rate of plane instill air.

Q: esin x dx secx

Q: The integral factor transforms the equation from not exact equation to an exact equation

A: We use the definition of Exact differential equation to obtain the answer of the given question.

Q: A spring attached to the ceiling is pulled 8 cm down from cquilibrium and released. The amplitude…

Q: do sin 0 – cos 0 cos 0

A: The given integral is ∫dθsinθ-cosθ

Q: Integral of 14x2/sqrt 49-x2 dx

Q: tan Find -dx using integration by parts.

A: Given integration ∫tan-1xx2dx

Q: A gas line-driven lawnmower has a blade that extends out 1 foot from its center. The tip of the…

Q: Water is poured into a conical paper cup at the rate of 3/2 in/sec (similar to Example 4 in Section…

A: Let the volume of conical paper cup be V in³, radius be r in, height be h in Given dV/dt=(3/2)…

Q: Give examples of basic integration using exponential rule

A: Give examples of basic integration using exponential rule Let us integrate an exponential function.…

Q: You are videotaping a race from a stand 132 ft. from the track, following a car that is moving at…

Q: how to use the apr approximation formula

A: For finding approximatel formula

Q: 6. tan (9x + 5) + C 1. O B. - O A. sec2(9x + 5) Which function should be differentiated? 6. tan (9x…

Q: An earthquake occurred at 9:40 A.M. on Nov. 1, 1755, at Lisbon, Portugal, and started a tsunami…

A: The given data is: The velocity of the wave is vw=540 ft/sec The period of the wave is: T=30…

Q: Water is pouring into an inverted cone at the rate of 8 cubic meters per minute. If the height of…

A: Given: Water is pouring into an invented cone at the rate of 8 cubic meters per minute. Height of…

Question

the saying that best explains how to integrate a function ∫x^n dx, where x cannot equal -1, by the simple power rule is

a) add one to the exponent and divide the expression by the new exponent.

b) divide the exponent by 2

c) multiply x by the two and then divide by 3.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

Expert Solution

Step 1

$G i v e n, \int x^{n} d x$

Step by step

Solved in 2 steps

Knowledge Booster

$Fundamental Theorem$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Determine dimension x to 3 decimal places.
How do you solve this integration question? I tried using trigonometric substitution but am lost.
can you pls show in present value formula
Use trapezoidal rule to solve this and work to 3 decimal Engineering and Numerical Analysis
(Integral sign) tan^4 x sec^6 x dx
Integral of tan^4(x)sec^6(x)dx
Give examples of basic integration using exponential rule
vertical cylinder is leaking water at a rate of 1m3/sec. If the cylinder has a height of 10m and a radius of 3m, at what rate is the height of the water changing when the height is 7m? Submit an exact answer in terms of π.
The radius of a circle is increasing at a constant rate of 2 meters per second. What is the rate of increase in the area of the circle at the instant when the circumference of the circle is 20pi meters? (It is at a constant rate of 2 meters per second, NOT .2 meters per second)
Find a curve through the point ( 1 , 5/6 ) whose length on the interval [ 1 , 2 ] is given by ∫ 1^2 sqrt(1 + 25 x^10)dx. \
Water is leaking out of an inverted conical tank at a rate of 7600 cubic centimeters per minute at the same time that water is being pumped into the tank at a constant rate. The tank has height 15 meters and the diameter at the top is 6.0 meters. If the water level is rising at a rate of 29 centimeters per minute when the height of the water is 2.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
Use substitution to integrate (calc 2 beginning) (show all steps plz)