dx using miscellaneous substitution will yield to secx + 1 Transforming A B © ² с -dz 1+z² © S²+ / de +2 D dz 1-z² S²=3 2-2z² -dz 1+z² 1+z² -dz

Q: Question We can apply General Power Formula of Integration on which of the following integrals? A…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

A: If a function F is an antiderivative of the function f then F'(x) = f(x) , and ∫f(x)dx=F(x)+C for…

Q: Question 28 dx Evaluate: Tx (x+1)log(x+1) 1 A -log² (x+1)+C 2 1 ® --In 10 log² (x + 1) + C B 2 (C)…

A:

Q: An equation of a hyperbola is given. (x+3)²-(y - 3)² - 1 9 16 (a) Find the center, vertices, foci,…

A:

Q: dy Classify the DE: xdx +xy= A) Separable and Linear (B) Separable but not Linear Linear but not…

A: Given differential equation is

Q: van [ f(x)dx = 5, [_o(x)dx=7, and [_n(x) dx = - -5 Which of the following can be determined given…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: √__(x+1) dx (x+2)(x-1)² 1 9 3 2 0-11/11 - 01/17 9 3 2 3 1 2 9 3 -io 1 9 - = 1[ A B + x+2 x-1 + C…

A:

Q: Given the integral sec6 (x - 1) tan4 (x - 1)dx, which of the following equatio useful for…

A:

Q: X lim x→1 x-1 Your answer x In x

A: Let's evaluate given function by using l'hospital's rule.

Q: In the indefinite Integral fin(cosh x + e*). sinh x tex cosh x + ex B) In(cosh x + e*) In(cosh x +…

A:

Q: Solve the integral: √√ 3√x dx x²

A:

Q: TL 2 Evaluate the integral: sin(3x)cos(3x)dx 3 1 A B C D H|m 3 16 1 3 16

A: To evaluate the integral. Option c is correct.

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A: Here we have to find the integral for finding the volume.

Q: [² -dx, determine all value/values of P for which the improper integral Given converges? (A) {0,1}…

A: The integral is ∫1∞ 1xpdx

Q: What is the differential equation corresponding to the general solution y² = Cx³. dy 2y = A dx 3x dy…

A: solution:-y2=Cx3where C is only one arbitrary constantdifferentiate both…

Q: sinh x tex cosh x + ex In the indefinite Integral in(cosh x + e*)- sinh x + ex A cosh x + ex sinh x…

A: In this question, we want to know the integrand of the given Integral.

Q: Find the volume of solid generated by revolving the region bounded by f(x)= x² + 1and g(x) =…

A: Volume

Q: Which of the following is a third degree partial differential equation? 3 дz J2z A др (В D др2 дz др…

A: given data  to find the degree of the partial differential equation

Q: Practical Question: An object is moving horizontally with the speed of 50 m/s. When the object at…

A: Projectile motion is the motion of an object projected horizontally into the air and moving…

Q: y=Arccos (x²)

A:

Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A: B option is correct.

Q: In the indefinite Integral in(cosh x + e*)- A sinh xte cosh x + ex sinh x + ex In(cosh x + e*)…

A:

Q: Find the volume of solid generated by revolving the region bounded by f(x)= x² + 1and g(x) =…

A:

Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

A: The correct answer is option (c).

Q: Question 10 Let f(x)=√3x-2 on the interval volume of the resulting solid. 43x 135 83m 125 83x 135…

A:

Q: Question 21 dx Evaluate: S (x+1) log(x+1) (A) In 10 log² (x + 1) + C 2 B In[log(x+1)] +C In 10 C…

A: We need to evaluate integral.

Q: y = x ¹ Arctan 4(x4)

A:

Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A: Definite integral Property : ∫ab fx±gx dx = ∫ab f(x) dx ± ∫ab g(x) dx. ∫ab k f(x)dx =k∫abf(x)dx ;…

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A: Here we have to find the integral

Q: B C) + et. + 4 (2x + 1)² 4 (2x + 1)²

A:

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3 A 355/20 cos²0de 0 **/2 B Ⓒ 18…

A: Evaluate using trigonometric substitution ∫-339-x2dx=?

Q: How many antiderivatives does a function of the form f(x)=x" have when n0? (A) none (B) may vary…

A: solution

Q: In the indefinite Integral Sin(cosh x + ex). integrand? sinh x + ex cosh x + ex dx, what is the

A:

Q: Which of the following can be determined given Ⓒx-d A (x) - )-g(x))dx (B S (4f(x) +9h(x))dx g(x)dx…

A:

Q: -Je cosx dx

A:

Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A: According to the properties of definite integral(A) ∫abkf(x)dx=k∫abf(x)dx      True(B)∫abkdx=k…

Q: Let f(x)=√3x-2 the y-axis and find the volume of the resulting solid. 83 (A) -unit ³ 135 83 (B)…

A: We will draw the curve f(x) and y=1. Points of intersectionf(x)=3x-2   and y=11=3x-2 1=3x-2x=1Point…

Q: √²/pdx. хр (1,00) B {0,1} C) (-∞0,00) D (-∞,1] Given (Α dx, determine all value/values of P for…

A:

Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A:

Q: A solid is formed by rotating the area between the curves y = x and y = x² between x = 0 and x = 1…

A: To solve this problem we use washer method.

Q: (x+1)dx (x+2)(x-1)² 1 / S If B -√2-1 + + *(x-1)2 ]dx. +2 dx, the values of A & C respectively are:

A: We can solve this as follows:

Q: (x+1)dx (x+2)(x-1)² S A 2 - x+2 B -1 + (x-1)2 ]dx. the values of A & C respectively are:

A: integration

Q: The improper integral ** ex dx is A Be (C) 1 D) 0 8

A: ∫0+∞e-x dx

Q: If f(x) = A B tanx 1+e 1+1² 1+e¹ In (secx) √ 1+tan²x 1+ e tanx sec 3x tanx -dt, then f'(x) equals

A: solution:-f(x)=∫0tanx1+t21+etdtApplying leibniz integral…

Q: •tanx √1+1² 0 1+e' sec ³x 1+etanx If f(x) = A B C D -dt, then f'(x) equals 1+tan²x 1+e' tan.x In…

A: Solved below

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ 3 A 2-unit² B -unit² с…

A:

Q: Q/IF 3= sin(X) (²314) y = 3² sin(x) cos(x) Prove that

A: To find y':

Q: •+∞0 The improper integral * fe 0 A) 0 B e C (D) 1 ∞ ex dx is

A:

Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A: C option is false

Q: 2 Let f(x)=√3x-2 on the interval axis about the y-axis and find the volume of the resulting solid.…

A: