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

Q: b. Stos-¹0 ¹(y) sinx √1+ sin2x dx dy

A: The given integral is, ∫01∫0cos-1ysinx1+sin2xdx dy. To find : Evaluate the integral. To evaluate the…

Q: (5-)dx ー3 2人 がー。 Sin(x) d X

A: 3)   ∫-34(5-x2) dx=5x-x24-34                                =54+3-16-94…

Q: |5sin(4x + 5) sin(2x --) dx

A: We need to evaluate the given integral. We will use the formula  Cos(A+B)-Cos(A-B)=-2 SinA SinB

Q: sinhx dx 1+ coshx ) A 1+ coshx B (1+coshx)? (1+coshx)² D 1+ coshx

A: We have to find

Q: S sin (2x – 1)cos (2x-1)dx (2х - 1)dx

A:

Q: x – sin 2x -dx x + cos2x

A:

Q: Integrate sinln (10x) dx X

A:

Q: cos (2x) dx sinx+cosx COS Evaluate:

A: the given integral is: ∫cos(2x)sinx+cosxdx we have to evaluate the given integral.

Q: /2 sin 2x dx Jo 3+cos (2x)

A:

Q: hpxp(₂h + x)us hx [V² [V² Find

A:

Q: 3. Sx² tan (3x-1) dx

A:

Q: (b) ( cosx) = -sinx dx

A: To Determine: find the derivative of cosx Given: we have a function cosx Explanation: we have a…

Q: (tan V) (sec V) b) Evaluate dx

A: Given integral: I=∫tan4(x)sec2(x)xdx

Q: csch (2 sin2x) dx 1. V1-4x² r(²-1)cos[cosh (In r)]dr OS 4.

A:

Q: x* + 4 dx : %3D 3

A:

Q: y=(sinx)x    d2y/dx2 ?

A: Apply exponent rule and solve:

Q: #4 tan lun sec x dx 4.

A:

Q: f(x) = sinx

A:

Q: csc² xcotxdx 4. S csc?xc 4-cot?x

A: As per bartleby guidelines we only give first question answers.

Q: sec? (1/x) dx. 9: (16pts) Evaluate

A:

Q: 2, " cos“(x)sin*(x)dx

A: To find : ∫0π2cos6xsin4xdx

Q: (Sin ² x - y) dx - tanx dy =o

A:

Q: -S * sin ´sin sin (e*) dx

A: we have to integrate

Q: T/3 1– sin x dx 1- sec x + T/4 cO X

A: Given: ∫π4π31-sec(x)+1-sin xcos xdx=∫π4π31dx-∫π4π3sec(x) dx+∫π4π31-sin xcos xdxSubstitute u=1-sin x;…

Q: Sx² cosh (1-x³) dx

A: Let the given integral be I - I = ∫x2cosh1-x3dx                   ............(1)Let,t = 1-x3…

Q: +* dx f. 3x +. i. 3x sin x' dx

A: To evaluate the given integrals by substitution.