Tutorial Exercise If fis integrable on [a, b], the following equation is correct. [" f(x) dr = limf (r.) Ar, where Ar- -x Use the given form of the definition evaluate the integral. Lo (1+5r) dr Part 1 of 6 Part 2 of 6 If x= -2, then each x₁ = -2 + 4x = -2+6✔ Since the interval is [-2, 4] and we have n sub-intervals, then Ax= Part 3 of 6 ·La. Using (1 + 5x) dx= lim /-1 b-a n n Submit Skip.(you cannot come back) 61 andz, =a+iAz. (1+5x) Ax, we have lim ✓ 6 m Σ (1 + 5(- ² + 5-)) ² − lim - - lim 2 (12

Q: e) S(secx + cotx)* dx 2.

A: To evaluate the given integral

Q: 180/take Find the indefinite integral. e' sintat sint+6cosđ TI37 e' +C -6sn&+cos&t +C 37 O(6sn&+cos&…

A: Consider the indefinite integral

Q: Evaluate the integral f tan³x sec"xdx Select one: sec"x O a. sec'x + c 7 O b. sec'æ sec'x + c 9 7…

A: Just we need to use the derivative of secx.

Q: Write the following expression in algebraic form: sin(arccos (6x)) V1-36z2 O VI – 36x² O VI – 6x² O…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Evaluate the integrals in Exercises

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Find div F and curl F if F(x, y, z) = 9ei - 3 cos y j + 2 sin² z k. div F= curl F=

A:

Q: 7) Evaluate the integrals a) 3(x + 1)²dx b) secx (tanx +cosx )dx

A: An indefinite integral, also known as antiderivative, is a function F(x)=∫f(x)dx such that…

Q: Express lim {5(x;)* – 6 tan°(x;)}Ax, n-+00 definite integral over the interval [-3,2n]. as a

A:

Q: 9. [(ti+e' j -te k)dt

A:

Q: sin*(¿e) cos* (e)də

A: This is a problem of indefinite integral. Based on the general formula of trigonometry we will…

Q: Convert the given expressions to integrable form. Do not evaluate the integral. 7) cosxsin(sinx)dx

A: Given, ∫0π4cosx sin(sinx)dx

Q: (x+2) dx 3-2x x2

A: Given integral is: ∫x+23-2x-x2dx

Q: An object is moving with a uniform acceleration a = 2ms ², determine the functions for: c) a)…

A:

Q: Prove that Simpson’s Rule is exact when approximating the integral of a cubic polynomial function,…

A: Given function is ∫01x3dx Let f(x)=ax^3+bx^2+cx+d, where a,b,c,d are coeffients. Now calculate the…

Q: Evaluate the integral. 30 sin(40) do

A: I=∫e3θsin⁡(4θ)dθ→(1)∫sin⁡(4θ)dθ=−cos⁡(4θ)4+Cddxe(3θ)=3e3θ+C

Q: Evaluate the definite integrals a) (бх? — - 2x – 10) dx = / (x+ 4)² dx = b) 1 c) (x* – x³ ) dx - ||

A: Some of the properties of integration  ∫abf(x)dx=F(b)-F(a) ∫xndx=xn+1n+1+C…

Q: We will try to compute the real integrale-1²/²e-itz dr. Let R> 0 and let y be the rectangle with…

A: As per the question we are given an improper Integral whose value we have to find by finding : The…

Q: Integral of cos2x on [0, infinity]

A: We have to use limits to find the given integral.

Q: What is the integral of f sin² x cos² x dx? cos(z) sin³ (2) cos(z) sin(z) + 4 4 ○ sin(4z)+4z 32 +C…

A:

Q: The Fourier integral of (-1, -14 < x < 0 1, 0<x< 14 0, otherwise f(x) = {

A:

Q: Q4. Evaluate the integral / V1- dr.

A: That's easy. Have a great day