dx (x + 2)3

Q: 7x2 V2x3 - 1 dx .2.

A:

Q: Evaluate the integral. 16 In(y) dy Vy

A:

Q: Evaluate the integral, if it exists.  ∫Csc2 (3t) dt

A: ∫ cosec23tdtLet 3t=θ⇒ddt3t=dθdt3=dθdt⇒dt=dθ3-1

Q: Evaluate the integral of ((x dx) / (x + 1)^8) from 0 to 1.

A:

Q: Evaluate the integral or show that it is divergent.

A:

Q: Compute the integral x 2 dx.

A: In this question we will use basic of calculus i.e concept of integration. We will use simple basic…

Q: 5. Determine if the integral is conve 0. exdx -1/2 V1-e 2x

A: Given query is to find integral converges or diverges.

Q: Evaluate the integral. dA, R = [0, 6] × [0, 16] x + 1

A:

Q: 2 dx x Inx 1/2

A: The given integral

Q: 1= [3y/7-3y° dy

A:

Q: Evaluate the derinite Integral. #5 In(x) dx

A:

Q: Find the integral J dx using the following methods: х2 — 9 -

A:

Q: Evaluate the integral by using a substitution prior to integration by parts. S(in 3x) dx O x (In…

A: First, we use the integration by parts.…

Q: Evaluate the integral using Algebraic Sub. x + a dx 3x a |

A: Just I have used the substitution to make integral easy and then solved it. Final solution is in the…

Q: Evaluate the integral 20 | by making the appropriate substitution: u = 5 – 2 (2³ – 2)® dx %3D -

A: Evaluate the integrals

Q: Evaluate the integral. inegral  0 to 1 [(x 3 -4x -10 )/(x 2 -x-6 ) ]dx

A: Consider the following definite integral:…

Q: Evaluate the integral / f(x) dx, where -1 -{ if – 1 < x < 0 if 0 < x < 1 -X - f(x) = 1-VT - x²

A:

Q: evaluate the integral using the methods covered in the text so far.

A:

Q: Evaluate the integral. dx 4 - x3

A:

Q: Evaluate the integral. (Use C fo ( 8x2 + 7x + 8 dx (x² + 1)2

A: Given integral is, ∫8x2+7x+8x2+12dx

Q: u. x + 3 2x³ - 8x -dx

A:

Q: Evaluate the integral or show that it is divergent.

A: Given: I=∫2∞dxxlnx                           ..1 for evaluating given integral, we substitute lnx=t…

Q: Evaluate the integral f 2x (x² + 3)° dx using the substitution u = x2 + 3.

A:

Q: -Зх сos 2x dx

A: Using Integration by-parts

Q: The improper integral 5dx is V1-x?

A: Since you have asked multiple, we will answer the first one. ∫015dx1-x2dxLet x = sin θ ⇒ dx = cos θ…

Q: Evaluate the integral J (Sx + 3x - 7* + 2)dx.

A: To solve the following integral

Q: 15. S(x + 2)²dx

A: Solve the following

Q: The improper integral 2dx is 1-x2 0.

A: π

Q: de 1+tan 0 k/2

A: Let I=∫0π2dθ1+tan θ      I=∫0π2dθ1+sin θcos θI=∫0π2cos θ dθcos θ+sin θ     ....(1)Using property…

Q: evaluate the integral.

A:

Q: Evaluate the integral a* In(x) dr

A:

Q: | 7x2 V2x3 - 1 dx

A: Here the given integration I=∫7x22x3-1dxNow Substitute as2x3-1 =u⇒6x2dx=duThus the integration…

Q: Consider the integral 7x – 21 da 2x – 3 If the integral is divergent, type an upper-case "D".…

A: the given integral is ∫027x-212x-3dx

Q: Evaluate the integral. integral 1 to 2   x  /  ( x+ 1) 2dx

A: Consider,

Q: evaluate the defmite Integral га (X -2)dx 4.

A: Given integral:

Q: By using u = In x, evaluate the integrals In x dx.

A: ∫x-1xlnx dx Now put, u=lnx⇒dudx=1x⇒du=1x dx

Q: Use the Trapezoidal Rule to evaluate the integral S |r| x²dx O 2 O -2 O 1 -1

A: Given Intergral ∫-11xx2dx. We have to find the value of it by using the Trapezoidal Rule. The…

Q: Evaluate the integrals by subs;tu;on dp- V5+x c)

A: ∫-14x5+x dx

Q: Compute the integral by algebraic substitution

A: we put 1-3x=u so that dx=-1/3du.and solve the question. see 2nd step.

Q: Evaluate the integral. 50x In(x) dx : + C

A:

Q: what is the integral of z 3^z dz

A:

Q: Evaluate the integral by making an appropriate u-substitution an applying any necessary formula(s).…

A: Solution:

Q: Use the form of the definition of the integral given in this theorem to evaluate the integral. 2 5x…

A:

Q: z · 3°dz

A:

Q: Evaluate the integral. 7 - x2 | x5y dy

A:

Q: (e2x –1)2 dx 1. e 2x

A:

Q: Evaluate the integral. x³In 4x dx

A:

Q: /1- xº V1-x°

A:

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.