solve both without using the table of integrals. Q1) integral of cos4xdx   Q2) integral of tan5xdx

Q: Use trigonometric substitution to find or evaluate the integral.

A: Given: The integral, ∫-12x24-x2dx.

Q: tan³ (2x) dx J cos4(2x)

A: Consider the indefinite integral  ∫tan32xcos4(2x)dx To evaluate the integral, first rewrite it using…

Q: (b) Evaluate the integral using by parts (* sin 2xdx formula:

A: Let I=∫x2sin2xdx. We have to evaluate the integral by using integration by parts.

Q: The value of the integral / (16 tan²z – 16 se²z)dz = . -6 O 96

A:

Q: rp= dx bo 1. to

A:

Q: 3 Which of the following is equal to sec ² x tan³x dx to obtain the correct indef inite integral?

A:

Q: sec® tan³Od0 5ød® coso

A:

Q: Use reduction formulas to evaluate the integrals ∫ sin2 2θ cos3 2θ dθ

A:

Q: sec2(Arctan x) dx 1+ x²

A: We have to use integration by substitution technique. we can use substitution for Arctan x.

Q: By using trapezoidal rule, n=2, The integral = π/2 sin (x) dx 0.9444 O 0.9481 O 0.94809 O 0.9482 O…

A:

Q: Evaluate the indefinite integral.

A: To evaluate the below indefinite integral.

Q: What substitutions are made to evaluate integrals of sin mx sin nx, sin mx cos nx, and cos mx cos…

A:

Q: What is the integral of cot^3(x)csc^2(x) dx?

A:

Q: Evaluate the following integrals. 13 1 sin²x -dx

A:

Q: Evaluate the integrals

A:

Q: 1 dx 4x2 +9

A:

Q: Which of the following is equal to sec 2 x tan³x dx to obtain the correct indef inite integral?

A:

Q: Can you calculate the following integral please.

A:

Q: 6z* cos (r*) dr-

A:

Q: 5. Evaluate the integral by using trigonometric substitution. x2 dx Vx² – 25

A:

Q: Solve the integral Sa 16 tani? 7+x²

A:

Q: Use the properties of integrals to choose the inequality that would make the statement true without…

A: We have to choose the inequality.

Q: [ sin³(2x) dx

A:

Q: 4 sin320 cos20 d0

A:

Q: 2- Solve the following integral with details 1 erlao cos? e r² dr sin@de ø do = x X = ? o 32ña

A: Given integral is  ∫02π∫0π∫0∞132πa05r3e-ra0cos2θ r2 dr sinθ dθ ϕ dϕ=x

Q: cot 4x dx V4 sin2 4x – 5

A: We have to evaluate the integral: ∫cot 4x4 sin2 4x-5dx Rewriting the integral, ∫cot 4x4 sin2…

Q: √1+4x4 x3 dx

A:

Q: Evaluate the integrals ∫sin 2θ - cos 2θ/(sin 2θ + cos 2θ)3 dθ

A: We have to evaluate the integrals: ∫sin2θ-cos2θsin2θ+cos2θ3dθ This integration will be solve d by…

Q: Evaluate the integrals below: 2 cos2x а) sin2x. [In(sin2x)]? + sin2x .dx, b) хе^.dy

A: We have to evaluate the following integrals,

Q: sin2t costdt

A:

Q: Evaluate the integral. 7/2 sin 8t sin 7t dt 16 O 31 O T5 3

A: the given integral is ∫0π2sin8t sin7t dt use the formula Sin C sin D= -cosC+D+cosC-D2 here C=8t and…

Q: Use a substitution to evaluate the following integral.  ∫ 6x 2 (fourth root 12 + 2x3 ) dx

A:

Q: Evaluate the integrals ∫sin2 2θ cos3 2θ dθ

A: Given:∫ sin22θ cos32θ dθ

Q: Evaluate the integral using the following values. Ca*dx = 1020, Sz dz dx = 30, C da = 6 %3D Solve :…

A: Given integral, ∫286x3-12x+5 dx

Q: Rewrite the integral using substitution: ₁x² cos(x³) dx 125 (cos u) du 25 ²5 (cos u) du 125 (cosu)…

A:

Q: 3 2. scc?x tanxdx

A: In this question we have to Solve the Integration.

Q: 2 sec" x AX JS -sec? x

A:

Q: Evaluate the integrals ∫8 cos3 2θ sin 2θ dθ

A: the given integral is: ∫8cos32θ sin2θ dθ we have to evaluate the given integral.   let the given…

Q: Evaluate the integral by using multiple substitutions. x² sin (9x2) Vcos (9x³) dx COS 25)

A:

Q: The triple integral ¹³(12xze²y²) dxdydz is equal to 3(e − 1) - True False O

A:

Q: Evaluate the integral by making the given substitution. sec(4x)tan(4x)dx, u = 4x + C

A:

Q: Sa cos6 x dx

A: We have to solve the problem

Q: V9x2 + 25 1.

A: Given: ∫9x2+25x2dxFormula: ∫fg'=fg-∫f'g;  f=9x2+25   ;    g'=1x2f'=9x9x2+25;   g=-1xTherefore,…

Q: 2. Reverse the order of integration and then evaluate. (''72 sin(ryldrdy a

A:

Q: why does the integral of cot(x) dx = ln((abs(sin(x)))? and is there a way to memorize it?

A:

Q: S yArc cos ydy

A:

Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. dx…

A: Given query is to find the integral.

Q: 5. | (2х + 3)V2x — 1dx

A: To solve the integral: ∫2x+32x-1 dx Solution: Let substitute t=2x-1. Differentiating both sides, we…