Question 23 Find the integral. [(3x2 - 4x + 7)dx A) бх — 4 + C (B 2x3 – 2x² + 7x + C x2 + 7x + C C 3 (D x3 - 2x2 + 7x + C |

Q: Integrate the given expression. [(4x + 2)2 dx A 16 x 3 + 8x 2 + 4x + C 3 B) 32x+ 16 + C (c) 16x 3 +…

A: ∫4x+22dx =∫16x2+4+16xdx =16x33+4x+8x2+c

Q: Let a = 6 and b = 6 What is the coefficient of x6y6 in (x + y)a+b?

A: This is a question of counting. One needs to find the coefficient in this fi ite expansion.

Q: 6. Complete the square to get an equivalent expression: 7-6x – x² No integration necessary on this…

A: 6 Given expression is 7−6x−x2. We have to complete the square to get the equivalent expression…

Q: Show that A×(BxC) + Bx(CxA) + Cx(AxB) =0.

A: We have to prove that LHS=RHS

Q: 3. S 2 x²+a² x4 = _ (x² + a²) ³² 3a²x3 -dx = + c

A:

Q: rỉ + 10x1x2 + x = as² + ßt²

A:

Q: Differentiate and simplify

A: The derivative of ln x is 1x.

Q: 3x Calculate: dx (x² + 2)² 3 а) + C 4 (x² + 2)² 3 + C x² + 2 b) 3 c) +C 4x2 + 8 3 + C 2x2 + 4 d) 1…

A:

Q: Stan and Ollie work on the integral J2x(a* + 2) di. Stan lets u = x? + 2 and proceeds to get (x + 2)…

A: Since, we have been given that Stan and Olie work on the integral:-∫2x(x2+2) dxIntegrating the above…

Q: 2. [Straightforward] Consider the 2 x 2 square [−1, 1] × [−1, 1]. Evaluate: 2x2 square [x² + y²] dA

A:

Q: Evaluate the integral: 5x/8x² – 1 dx - 5 (8x2 – 1)- + C (8a? – 1)-+ C (822 – 1) + C -(8x2 – 1) + C 8…

A:

Q: A rectangular poster has an area of (2x + 3x - 10) square inches. What are the dimensions of the…

A: We can find the dimension of the rectangle as below.

Q: (x* + 1) (x²-2x ti>

A: Given  I=∫dxx2+1x2-2x+1 Apply partial fraction decomposition 1x2+1x2-2x+1=Ax+Bx2+1+Cx+Dx2-2x+1…

Q: Evaluate the Integral 2. S V5 + 12x – 9x²dx - ANSWER: 2. (3x-2)v5+12x-9x²+9Sin¬13*- 2]+C (3х-2)

A:

Q: Differentiate 4(x + 2y)2 = x2 + y2

A: given equation 4(x + 2y)2 = x2 + y2

Q: Evaluate the integral (2a+4)(x² + 4x + 2)*dx 4 by making the substitution u = x+ 4x + 2. ,2

A: Let u=x2+4x+2, now differentiate it with respect to x. du = (2x+4)dx So,…

Q: dt t² - 8t + 20 +2

A:

Q: Evaluate the integral fe (2x+4) (x² + 4x + 2) dx n- by making the substitution u = x²+ 4x +2.

A: In the question we have to find the integral of the given function.

Q: b) 3 +4 1.

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: 5л — 2 dx x2 +1 10.)

A:

Q: 1. Evaluate: f (2x+3)dx x²+2x+5

A: As per our guild line we are supposed to answer only one question please repost other questions as…

Q: Please find cross product c=a x b, where a= and b =. For c=16i+0j+?k, please enter the missing k…

A:

Q: 1 x+1 ST (2y-2)dydx Evaluate 0 °0

A:

Q: ' EVALUATE (a) lem x² I メ→ 43×キ3x+1」 メナー* ×43x43x+1 (C) lem x2i 7ー ×+」

A: Given: (a) limx→-1- x2-1x3+3x2+3x+1(b) limx→-1+ x2-1x3+3x2+3x+1(c) limx→-1 x2-1x3+3x2+3x+1  To find:…

Q: S x³√x²-7dx X X 3

A:

Q: dx 10) √x²4(14+x²) a) - - - c) - 1 4X ㅗ 4x + 1 andan ²/3 + c autan 1/2/3 + c 8 I ondan 2/2 + c 8 j 8

A:

Q: A rectangle with length / and width w has a diagonal of D inches. If the perimeter of the rectangle…

A:

Q: Prove that

A:

Q: 8. 2dx 3 3x

A: Given

Q: 42 x2 dx =. V(73 + 14) 42 / (x3 + 14)+ C V 28 V (x3 + 14) + C 14 (x3 + 14) + C 84 / (x3 + 14) + C

A: From the basic integration

Q: Evaluate the integral 2x + 5) (x² + 5x + 9) ³dx by making the substitution u = x² + 5x +9. + C NOTE:…

A: ∫xndx=xn+1n+1+cdxndx=nxn-1let x2+5x+9=u

Q: 5x - 9x +6 dx x - 2x +x

A: Solution of the problem as follows