A study, in early 2000, said the typical American's annual income is changing at a rate of r(t) = 30(1.003)* dollars per month, where t is in months from January 1, 2000. Write down the integral that shows how much the typical American's income changed during 2000. Take t = 0 to be January, 2000

Q: Find the indefinite integral by using the substitution x = tan 0 (1+ x2)2dx

A:

Q: What is the value of the definite integral, ¿ xp- 「京+Na-x

A: Given integral, ∫0axx+a-xdx

Q: Find the indefinite integral by making a change of variables

A: Given integral is By using the following substitution , we get

Q: Evaluate the following and use change of bounds for definite integrals when appropriate.

A:

Q: Find the indefinite integral. est dt = +C.

A:

Q: What is the definite integral of a function ƒ over a closed interval3a, b4 ? When can you be sure it…

A: The definite integral of a function f(x) over a closed interval [a,b] is a real number  denoted by…

Q: Find the indefinite integral by making a change of variables.

A: Given: ∫(x+1)2-xdx

Q: Use an appropriate substitution to evaluate the following definite integral:

A:

Q: Evaluate integral of dx/x-2 from -6to-10

A:

Q: Find the indefinite integral of the following functions :

A:

Q: What is the integral of a function e raised to the power -n .?

A: topic- integration

Q: Find the most general antiderivative or indefinite integral. dt

A:

Q: Evaluate the definite integral using the properties of even and odd functions. dt

A: Given the definite integralI=∫−22(14t6+7)dt

Q: For dt, use a change of variables to evaluate the definite integral.

A:

Q: Which of the following is an improper integral?

A:

Q: se sec³ xtanxdx

A: we have to solve integration

Q: Write the integral as a sum of integrals without absolute values and evaluate.

A: If we have integral , such that ∫a1a2f(x)dx , then this integral can be written as ∫a1a2f(x)dx  =…

Q: Find the indefinite integral by using the substitution x = 9 tan(0).

A:

Q: Find the indefinite integral and check the result by differentiation.

A: |The indefinite integral ∫(4t2+3)2dt

Q: Find the indefinite integral by making the appropriate change in the variable. a) Sx²Vx³ +1 dx 1+4x…

A:

Q: find the indefinite integral of (3lnx)/x dx

A:

Q: Evaluate the definite integral two ways: first by a u-substitution in the definite integral and then…

A:

Q: What does the integral sign represent?

A: Consider  ∫f(x) dx

Q: What is the definite integral of a function ƒ over a closed interval [a, b] ? When can you be sure…

A:

Q: Since YouTube first became available to the public in mid-2005, the rate at which video has been…

A:

Q: 3x dx

A:

Q: evaulate the definite integral

A:

Q: L²x√x-2dx

A:

Q: S18x°-メ 1)x +5メ-1

A: ∫(8x3-x2+5x-1) dx

Q: | Suppose that the net earnings of a particular company at time t are being generated at the rate of…

A:

Q: Find the indefinite integral by making a change of variables. |(x + 6)V5 - x dx

A: Given integration is : ∫x+65-xdx To find the value of given integral

Q: Evaluate the indefinite integral by using by part technique 4x dx 4. b. 4xe

A:

Q: |10dx 1

A: The integral function is ∫11110dx.

Q: Find the indefinite integral.

A: It is given that, ∫e-1t3t4 dtWe have to find the indefinite integral.

Q: What is the difference between an antiderivate of a function and the indefinite integral of that…

A: An anti-derivative of f(x) is just any function whose derivative is f(x) whereas an indefinite…

Q: find the indefinite integral of

A:

Q: Find the indefinite integral by making a change of variables

A: Consider the given integral as ∫x3x3-1dx

Q: Evaluate the indefinite integral x5 - 5x dx x3

A: This is a simple question related to integration  Solution is given below

Q: a+bx² √3ax+bx³ dx

A: This question is related to indefinite integration, we will solve it using given information.

Q: State the rules for approximating the definite integral

A: To State: Rules for approximating definite integral.   Definite Integral: An Integral with upper and…

Q: Find the general indefinite integral

A:

Q: Se dt

A:

Q: How do you evaluate this integral?

A: Given integral is ∫01xsinnπxdx

Q: Find the indefinite integral of Jsec²x tanx√1 + tanx dx. 22/2

A:

Q: Evaluate the indefinite integral x5 – 5x dx x3

A:

Q: A water quality control agency estimates that a certain factory discharges pollutants into a river…

A:

Q: Find the indefinite integral by making a change of variables. ∫x√(x + 6) dx

A: The given integral is ∫xx+6dx

Q: If finding the integral of 1/x does the x need to be in absolute value bars in the answer?

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.