100. Given that f₁² xdx = 11/1, 2 S₁² x² dx = 2 1/37, and ₁² x³ dx = 1, 3 4 Compute ¹ (1 - x)² dx

Q: 3. | (1- 2x) dx 0.

A: Given that, ∫01xdx=12 ∫01x2dx=13 ∫01x3dx=14 The integral to be evaluated is given as, I=∫011-2x3dx…

Q: 1. dx nx e

A: Let I=∫1x(ln x)2dx

Q: X-1 (x - 2)² 5. S dx

A: We have to evaluate the integral.

Q: 3. (1+2x − ¹) dx (assume x > 0)

A:

Q: 1 5. S z dx x²(5+x)3

A:

Q: 2. Count 1-e-x2 dx x2 -1 to an accuracy of 3 decimal places after the comma!

A:

Q: 2X Y=ln (3") +sec (Inx)+tan (ln5x)

A: We will differentiate the function and simplify.   The detailed solution is as follows below:

Q: 3. (2 + ln x)³ √ (2+1) X A. (2 + ln x) 4 +C -dx C. (2 + Inx)³ + C 4 {1tinx? Syn (2+1mx) +C 20 B. (2…

A: We can solve the integral using substitution method. Here we substitute 2+lnx by z and then apply…

Q: /0 1 X-4 x2 – 5x + 6 dx

A:

Q: Show that

A:

Q: 10 1/3 Evaluate I = - 2) dx 13

A:

Q: 1. dx Jo (x2 + 4)3/2 8.

A:

Q: 1) Evalvate - 5 dx ZV5 arctan x - 5 5 2 /5 arctan X-5 +C 2 x* - 5 arctan 5 arctan 25

A:

Q: In x dx dx х 2** n* dx

A:

Q: xx (x)dx X 3TT 28

A:

Q: 1. Find dx if it exists.

A:

Q: ?cos(xy)dxdy

A: The objective here is to evaluate the double integral: ∫01∫0πx2cosxydxdy

Q: 5. [x³5 (2²³ + x5 (x³ + 1)6 dx

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Determine dy/dx y = (In 2x) - (ln(3x + 1)) 1 3x²+x 3x 1 None of the choices 1 3x²-x

A:

Q: 4 S. x* - 6 dx = 14

A: Let, I=∫x4−6x14dx ⇒I=∫1x7x4−6dx ⇒I=∫x2x71−6x4dx ⇒I=∫1x51−6x4dx

Q: Compute the following.   d/dx(3x+5)2 x=1

A:

Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

A:

Q: 1. (x+6у?)dx - 4хydy-0

A: Given problem:- (x2 + 6y2 ) dx -  4xydy = 0  Solve the given differential equation

Q: da Vx(1+ x) 1. 8.

A:

Q: What is the value of 1 a x2 evaluated between 2 and 5 if the constant a=4?

A:

Q: 1 ,-(x-a)/b dx a

A:

Q: 3 S Inx dx 1

A:

Q: SOLVE THE FOLLOWING 1. dx 4x²-4x-5 2. dx=√(x² - 2x + 3)³

A: 1. dydx=14x2-4x-5…

Q: ng Table 1 w — o o S

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: . S(x + 1) · 3*². 32x+1 dx

A:

Q: 1 dx O (1+ x)1/4 1.

A:

Q: -3 In (x) dx

A:

Q: 2 6. S dx 0 1-x

A:

Q: Calculate 1 10 1 x² dx.

A: