If (x+1) dx (x+2)(x-1)² S -=S= A B + x + 2 + x-1 C (x-1)2 dx, the values of A & C respectively are:

Q: 1 Solve the integral: J 3 x + x 5 6 x In|1+ A +C + C Shi+x+c 6 1+ C 5 1+x8 +c +C B C 516 In|1+ - dx

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Q: Solve the integral: eln(2x²+3 +3x-4)³( (4x + 3)dx (2x²+3x+4)² + C A 4 (2x²+3x+4)*(4) 3 + C eIn(2x² +…

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Q: How many antiderivatives does a function of the form f(x)=x" have when n*0= A) infinitely many (B)…

A: We have to choose option find antiderivative

Q: x+2 Determine the case of the following proper rational function after simplification: (x² – 4)(x³ –…

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Q: Given √ 1 pdx.c A (-∞,1] B (1,00⁰) Ⓒ (-∞0,00) D (0,1) dx, determine all value/values of P for which…

A: This can be solved as follows:

Q: Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

A: Given, ∫ 9/√(x2+6x-7) dx We can calculate using substitute method

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

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Q: Determine the area bounded by the functions f(x)=(x + 1)3 and g(x)=x+1,

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Q: Question 5 The improper integral A e B) 0 (C) D 1 8 +∞0 Se ex dx is

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

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Q: 15 S A B (c) D (x+1)dx (x+2)(x-1)² 1 2 -- 9 1 2 " 9 3 -lo 1 9 " - - W|N 2 1 9 3 W|N 3 -S[₂ = A B +…

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Q: If g(x) = -S^*[e²− ln(2t+1)]dt, find g''(x) . dx 2 (A (2x + 1)2 Be* -In(2x+1) 4 (C) Ce¹+ (2x + 1)² 4…

A: Here is the solution of the given problem.  By using derives under Integral.

Q: dx S secx + 1 1+z² Ⓒ √ 1+ 2²/ dz S A 1-z² -z² B 1+z² © √²/²+²/d² S³ -dz 1-z² 2-2z² / 1²= D 1+z²…

A: Note: According to our expert guidelines only first individual question is to be answered kindly…

Q: Which of the following can be determined given 3 A - (f(x) = g(x))dx B (4f(x) +9h(x))dx 3 © (f(x) +…

A: g(x) is integrated in the interval 0 to 3 f(x) and h(x) are integrated in the interval 0 to 3

Q: Question 2 Solve the integral: A √√x 3 B 33√/ x² +C 3√x² +C 6 6√√x +C D √√ 3√x dx

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Q: Question 15 Evaluate the double integral: (A) 40 B) 80 C) 60 (D) 30 ²² 6) (3x² +9y²) dxdy

A: we can find the double integral.

Q: Question 37 1 Solve the integral: S- dx √√√√x+x A m/1+ + X +C ℗ 6n/5+x²³| +C B Ⓒ1+x²+c с X C =…

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

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Q: √²² (3x² +9y²) dxdy Evaluate the double integral: (A) 40 (B) 80 Ⓒ30 (D) 60

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

A: We have to find out the solution

Q: 1 Solve the integral: S dx 3 x ที่ X + X h_1+x+c A C Ⓡ 6ın|5+x=³² | +C B © h1+x8 l+c + C h1+x+c D +…

A: Given that we need to solve the following  integral.

Q: If f(x) = f = Stanu √I+1² 0 1+e' In (secx)√1+tan²x (A) tanx 1+e sec ³x В) Ⓒ (D) tanx 1+tan²x 1+e…

A: Application of integration

Q: To evaluate the integral sin ³0cos 0d0 by trigonometric transformation, we use the identity; A…

A: ∫sin3θcos6θ dθ

Q: X+2 Determine the case of the following proper rational function after simplification: (x²-4)(x³-8)…

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Q: 15+0. The improper integral e* dx is

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

A: We have to choose correct option

Q: Question 20 How many antiderivatives does a function of the form f(x)=x" have when n*0₂ (A) 1 (B)…

A: Antiderivative means Integration

Q: S Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

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Q: Determine the integral: x²cosxdx A x²sinx + 2xcosx-2sinx + C B x²sinx-2xcosx-2sinx + C C…

A: integration

Q: Evaluate the double integral: S²² (3x² +9y²) dxdy 0

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Q: Evaluating √9-x² dx using trigonometric substitution will lead to: [/2cos²0do (A) 18 9[*/ cos²0d0 B…

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Q: 2 Let f(x)=√√3x-2 on the interval y-axis and find the volume of the resulting solid. 43x A -unit3…

A: Let's find volume of solid given curve.

Q: 17. Evaluate [9e³x dx O9e³c+1 3c+1 O9e3c O9ec-3 3e³c-3

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1. A unit² B D H|m -unit² 3 q…

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Q: If g(x) = d __*[e' - In(2t+1)]dt, find g''(x) . dx -2

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Q: Which of the following is NOT a method for finding volume of solids of revolution? A) washer method…

A: Conic method

Q: Question 4 9 Let the integral be 'solvable' using trigonometric substitution. What is the correct…

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

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Q: If the Laplace transform of f(t) = e cos(et) + t sin(t) is determined the a. a shifting theorem can…

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

A: A option is correct.

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

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Q: x²+3x-7 X-2 +5x+31n|x-2|+C + +In|3x-6|+C 2 x²+5x+In/3x-6|+C x² + 5x + n/x-21 +C 2 3 In Evaluate the…

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Q: Evaluate the improper integral (A) diverges B (Q) Na O ساح 3 1²23 -dx

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Q: √ Given A B CO f(x) dx = 0 and 11 55 6 √ √²+ f(x) dx = 1/201₁ 11 6 , evaluate √3 3f(x) dx - ₁2 f(x)…

A: To solve the integration using properties and given data.

Q: e: Sz dx (x+1) log(x+1)

A:

Q: tanx If f(x) = (Α) B C D S 0 sec ³x 1+etanx In (secx) √ 1+tan²x tanx 1+e sec²x 1+ etanx 1+1² -dt,…

A: Here, given that: f(x)=∫0tan x1+t21+etdt...(1)

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: antiderivatives does a function of the form f(x)=x" have when n*O? may vary depending on n How many…

A: Formula: Antiderivative of xn = xn+1/n+1

Q: Question 14 dx Transforming - using miscellaneous substitution will yield to secx + 1 1-z² A 1+z²…

A: Here we have to transform the given integral by using miscellaneous substitution.