Q4. (a) Evaluate the definite integrals: (i) ſ(2 – 5/1 – x² }tx_ (ii) [sin 2x cos 2x dx (iv) [": 'V10x - x² dx 1 – 1, if x20 х — (b) Given f(x)= Evaluate (i) [ f(x) dx (ii) [f(x) dx x +1 if x < 0 -1 -5 dy = e; y(0)= 2 dx (c) Solve the initial value problem

Q: 2. (a) Find the derivative of f(x) = 2x2 – 2x + 2 from first principle sin x (b) If y = x + find x4…

A:

Q: - 9 √²x²=2 dx = √² ((x² + 1) = 10) dx 1 + 10 1 +

A: ∫01x2−91+x2dx=∫01((x2+1)−101+x2)dx

Q: 10. | [3 - e-lxl – cos x + log(x²)]dx = 0 x³ +4x – sin x 11. x² – 7 -dx 3 0

A: 10. ∫a53-e-x-cosx+lnx2dxEliminate absolutes =∫a53-e-x-cosx+lnx2dxApply the Sum Rule:…

Q: 77. er = 1+ x20 + 20 +...

A:

Q: Given x+ y +z= 5 and Po(2,2,1), find the following. (a) Find the equation for the tangent plane at…

A: Here is the solution

Q: 2x

A:

Q: Inx (a) log₂x = In2 (b) dx =

A: We have to prove that: (a) log2x=lnxln2 (b) ddxtan-1x=11+x2

Q: Q1) Evaluate: (a) fe²_1_dx Inx sin ¹x 1-x² dx (b) f 1- cos dx (e) Jỗ 2sinx cosx dx (c) | Inx dx

A:

Q: Differentiate h(x): sin¬'(x) 1+x

A:

Q: Find f'(x) for f(x) 8 sin(x) 5x2 +8 sin(x)

A: We have to find

Q: Determine f(x) so that cos(In x) f(x) dx = sin(In²x) + C

A: Option B

Q: : (a) Evaluate S cosx sinx V1 – sin+x_dx. (b) Evaluate S V1 – x² dx.

A:

Q: Evaluate (i) dx S √e xlnx√(2lnx)² – 1

A: We are asked to evaluate the integral

Q: (a) [In(4) - 2e¹³] dx d b) dx d (c) [2²² - 1 (2²)] = 4e³x In(x [sec (12r) + tan-¹(2x)]

A: NOTE: Refresh your page if you can't see any equations. .

Q: Find the indefinite integral: csc (x) dx csc (x) - sin (x)

A: We have to evaluate the following integration.