x³ dx 3. S V(x2-9)3 (x²–9)3

Q: Jse the properties of integrals to verify the inequality. 1 ,2 x cos I dx <1

A: Given query is to find integral to verify the inequality.

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. COS s*(7t)…

A:

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A: Consider the integration ∫x3x2+9dx Substitute x=3tanθ ⇒dx=3sec2θdθ Hence,…

Q: Evaluate the integral. 17 dx 2 Vx² – 1 - NOTE: Enter the exact, fully simplified answer.

A: Let's find.

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 9e" + 8e-X dx…

A:

Q: 1e uex dx (3+x²)5/2 x3 Ue be

A: ∫03x33+x252 dx Consider, ∫x33+x252 dx Put, x=3 tanθ⇒1=3 sec2θ·dθdx⇒dx=3 sec2θ dθ Therefore,…

Q: Q2) Evaluate the following integral using Trigonometric Substitutions Method: dx y 9x² + 16

A: To evaluate: I=∫dx9x2+16 Substitute x=4sec u3⇒dx=43sec u tan u du

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A: Given I=∫x3x2+81dx       Put x=9 tan θ            dx=9 sec2θ dθ      I =∫9 tanθ3 9 sec2θ…

Q: (a) Evaluate the integral using the substitution u = In (5x). x In (5x) dx x In (5x) ? Edit +C (b)…

A: An integral in some cases can be simplified using a substitution. For example ∫ln(x)xdx with the…

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A: Topic- Integration

Q: π 7. fz sin¹x cos¹ x dx

A: To evaluate the following integral by using Walli's formula.∫0π2 sin4 x cos4 x dx

Q: Evaluate the integral. (Use C for the constant of i 4x2 + 3x + 4 dx (x² + 1)2

A:

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A:

Q: 4 x*dx J (x² + 1)²

A: Solution is given below:

Q: Find or evaluate the integral using an appropriate trigonometric substitution. +3 x2 dx 4 + C

A:

Q: Evaluate the integral using the given substitution. Sx cos (10n2) dx, u = 10x² sin (10x²) - C sin…

A:

Q: Evaluate the integral using the given substitution. (Vx cos (x3/2- 4) dx

A:

Q: x 4 dx (x²+4)² S

A:

Q: TU 8. fz sin¹x cos5 x dx 2 0

A: To find the value of the given definite integral:∫0π2sin4x cos5x dxWalli's Formula:∫0π2 cosnx dx=…

Q: d sin – x2)dx dx V/ Tx

A:

Q: Write as an integral on the interval 0, the expression represented by Зл lim,0o E (2x – cos x;) i=1…

A:

Q: J zV -1 2.

A:

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A: Consider the integral

Q: Evaluate the integral in terms of inverse hyperbolic function x2 dx Vx² + 1

A: for a part see 2nd,3rd and 4th step. for b part

Q: Find the integral using an appropriate trigonometric substitution V25x2 – 1 dx x4

A:

Q: 1. S dx x² Vx2+4

A: In this question we will use basic of calculus i.e concept of integration. We will simply integrate…

Q: 9 Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

A: We have to solve

Q: Using the substitution = the integral reduces to -1) 1 2p- dz 1/3

A:

Q: Evaluate the integral. 19 dx x²/x² NOTE: Enter the exact, fully simplified answer.

A: Let I = ∫2219 dxx2x2-1

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A:

Q: хах 2. S (V16-x2) 3

A:

Q: Evaluate the integral. 19 dx x²Væ² – I NOTE: Enter the exact., fully simplified answer.

A: To evaluate:∫2219x2x2-1dx

Q: Evaluate the integral f x2 dx V36–x² using trigonometric substitution. Note: Use C for an arbitrary…

A:

Q: Q4) Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx y =

A:

Q: Evaluate the integral (Trigonometric Substitution) 1 (n²z6 – z®)ždz

A:

Q: f(cos*x- sin *xkx *a

A:

Q: dz 3x2 +8

A:

Q: V9x² – 25 53. dx, x > 3 +3

A: consider I= ∫9x2-25x3 dx

Q: Evaluate the integral. 3 sin x dx +C |3D

A:

Q: Evaluate the integral 25 6)"dx - by making the substitution u = x -6. + C NOTE: Your answer should…

A:

Q: TU 2. fz sin² x cos4 x dx J

A:

Q: Evaluate the followaing integrals Li (1– 2sin?(x).sin(4x) dx) |

A:

Q: Evaluate the integral. 3 sin-x dx +C %3D

A:

Q: dx (d) Evaluate the integral | using trigonometric substitutions. X²V4X +1

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the integral ∫ x/ √(1 − x2 )dx using u-substitution.Then find the integral using trigonometric…

A: Given: ∫x1-x2dx

Q: Evaluate the integral if it exists. dx Select the correct answer. 1 1) x- 2 lnx-+ C 2) 2- Inx+ C 3)…

A: We use identity  (a-b)2= a2+b2-2ab in numerator of integral

Q: 2 58 n lim dx !! (n+1)? j=1 and the value of the integral is

A:

Q: Using appropriate substitution and taking a + 0, 3tan(ax) the integral S dx is equal to: cos² (ax)

A:

Q: Evaluate the integral f v96 + 16x² dx using trigonometric substitution.

A:

Q: Evaluate the integral (Trigonometric Substitution) 4 x*dx (x² + 1)²

A: