1. (a) Evaluate Jo 0 r* - ¹ (1 − x6) 15 (1+x) ¹5 -dx.

Q: Find + 7)(x – 2)dx

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Q: |x + 7| X < -7 X + 7.

A:

Q: X(35X [En(x) ? dx

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Q: 2x + 1 (b) √ ² (1 − x) -dx

A:

Q: x +4 x² + 2x + 5 -dx

A: To calculate the integral ∫x+4x2+2x+5dx.   Use the common integrals:…

Q: Finally, use the Generalized Power Rule to determine[x -x], noting that x-x is the difference of two…

A: Here we have to find differentiation of f(x)

Q: 1. (a). Show that (1 · 1) + (0 ∙ 1 + 0) = 1. (b). Find the value of (1 + 1) .

A:

Q: 8 √₁ 2 4-x² 4 x² 2 +4.x² dx

A:

Q: ∫((e3x)/(5+2e3x))dx

A:

Q: d, 3 Find dx -)- + x(х - 1)). A -3 +2х-1 B +1 -3 +1 -6 +2х-1 x3 (D

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Q: 3. 1 x2+12x-5 (x+1)(x-7) dx

A: We need to solve the following integral I = ∫x2+12x-5x+12x-7dx…

Q: What happens to this base function that went from  a(x)= x2 to  h(x) = -x2+ 4 and why it happened?

A: The objective of the question is to understand the transformation of the base function a(x) = x^2 to…

Q: -8x? + 16x + 8 dx (x – 1)2(x² + 1)

A: We will solve the problem

Q: Evaluate: 3 f(-x² + 4x-1)dx 1

A:

Q: 2 [+√²-1)dx (4) »

A:

Q: 3 7) Evaluate: f(-x² + 4x − 1)dx 1

A: Given, ∫13(-x2+4x-1)dx

Q: + 9x + 27 dx (x + 3) (x² + 9)

A:

Q: [ (1 + 2x) dx 12

A: The given integral is ∫25 1+2x dx. Evaluate as follows.

Q: - A) -16x-5-x-2/3 C) 3 4) Find: d 4 dx x4 5 -4/3 B) ਪ੍ਰੈਲ-5-1582/3 D) - 1 5-2/3 433 3

A:

Q: Evaluate x2 dx

A: Use rules of integration

Q: 81 +x + 41 -x Evaluate

A: Introduction :--

Q: 20 x3 25+x² 2)골 2 dx

A:

Q: 2 X 2 X 0+ - 4 +4 dx =

A: C+C

Q: Q3. Evaluate S 2x+1-5x-1 dx 10*

A: Given that ∫2x+1-5x-110x dx evaluate the integral

Q: Compute the following. S(24x-8) (24x -8)(6x²–4x – 9)ª dx

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Q: ex - 32 √x +x 22

A:

Q: Integrate the following x2(x-4)ex(x-2)

A: find out the integral of x2(x-4)exx-2

Q: Find 4 of 3xy –- x³ = 5 at (1, 2)

A: Given; 3xy-x3=5 at (1,2)

Q: x² – 4 Evaluate: O -V-4+2sec-() +c (A + C B = 2/ x2 – 4 + sec + C = /x² – 4 + sec (4) c) + C -Vx² -4…

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Q: -10 b) L,(x² + x)dx 10

A:

Q: ∫(x+4)dx/x2+16

A: To integrate: ∫x+4x2+16dx ∫x+4x2+16dx =∫xx2+16+4x2+16dx--------(1)…

Q: 5 Evaluate [ (x + 2)(x² - 1) dx

A: Solution:Given   let      I=∫25(x+2)(x2-1)dxFormula:∫xndx=xn+1n+1+C