15 Evaluate the integral (10 + sin t)" cos t dt using the substitution u = 10+ sin t. + sin t) cos t dt 15

Q: 5) find the integral J8 sin 2x * cos2x dx

A: see below the calculation and answer

Q: 3. Find the integral (a) f(cos(x) + sin(x))² cos(2x) dx 1/3 /tan(x) (b) dx sin(2x) tan-¹(x) dx (d)…

A: (a)  I=∫cosx+sinx2cos(2x)dx =∫(cos2x+sin2x+2sinxcosx)cos(2x)dx =∫(1+sin2x)cos(2x)dxHere, Let…

Q: 7. Prove: sin(t) dt sin(1) + cos(1) 4

A:

Q: 18 Estimate the error if cos t is approximated by 1- 2 in the integral cos t? dt. 4! - -+ The error…

A:

Q: The f sin 2x cos 2x dx is 1+3 cos 4x 1 sin²4x + C 24 1 In|1 + 3 cos 4x| + C 12 {A} {B} {C} - In|1 +…

A: To find the value of the given integral ∫sin2xcos2x1+3cos4xdx using substitution

Q: Evaluate the integral. |cos 7x cos 3x dx

A: The given integral ∫cos7xcos3xdx.

Q: 4. Evaluate the integral. S tan (2x) sec°(2x) dx

A:

Q: 5) Evaluate the integral: tan 3 x dx

A: Given integral, ∫tan3x dx

Q: 5. Evalvate the Intgral S2 cos (2x) - Sin 2x)=

A: To evaluate the integral: ∫2cos22x·sin22x dx Solution: We know that, 1). 2sinθ cosθ=sin2θ 2).…

Q: Evaluate the integral f sin²(3x) cos (3x) dx.

A: The given integral is ∫sin23xcos53xdx. We have to evaluate the given integral.

Q: Evaluate the integral: 2 sin(3x)cos(3x)dx A B 1 4/6 —— 1 wlr 3 1 - wlw

A: Given ∫π3π2sin(3x)cos(3x)dx

Q: T/3 3 sin (3t) -dt. 5 - cos (3t) Evaluate the integral

A:

Q: 15. Use a suitable change of variables to determine the indefinite integral. [1²cos² (1³) sin(1³)dt

A:

Q: Find the indefinite integral. |cos 2x ein 2* de sin 2x A) 2 +C ein 2x +C B) C) sin 2x e cos2x +C D)…

A:

Q: 27. tan'x sec x dx 30. tan r dt

A: the basic formulae must to solve these problems: 1) ∫xn dx =xn+1n+1+c2)d tan(x)dx= sec2(x) 3) d…

Q: 15. cot x cos²x dxr 19. r sin'r dt

A:

Q: Evaluate the integral. n/2 | [2 cos ti -3 sin 5t j+ sin? 3t k] dt 0. n/2 | [2 cos ti- 3t k dt = cos…

A: Integrate

Q: Steb by step

A: We will need integration by parts for this problem. So we assume u and dv and from there find du and…

Q: Estimate the error if cos t² is approximated by 1 integral , cos r² dt. 4! in the 2

A: We have,

Q: Integrate with respect to x: sin(3r) b 2 cos(4x) cos²(2x) a

A:

Q: 8. 1² sin Bt dt

A: We can evaluate the given integral by using the   integration by parts method.

Q: Solve the integral / cos 10x de 1 sin(10x) + C 10 sin(10) + C 1 ·cos(10x) + C 10 1 sin(10x) + C 10…

A:

Q: 3 4. sin x cos xdx

A: These formulae are used while solving the question:

Q: the integral F(®) = cos*(0) + sin(20) – 3 cos(0) COS do sin (0) +3 cos2(0) + 2 sin(0) – 3

A:

Q: Evaluate the integral (10 + sin t)* cos t dt 14 using the substitution u = 10 + sin t. 14 10 + sin…

A:

Q: Compute the definite integral T/4 0 5 sin² (3x) dx

A: Sol:- ∫0π45sin23xdxTake the constant out:  ∫a·fxdx=a·∫fxdx=5·∫0π4sin23xdx=5·∫0π4121-cos6xdxTake the…

Q: Classify and Solve; +9 = cos² t + sin² t + cosh t + sinh t + 3 sin t – 3t dt dt2

A: d2ydt2+9dydt=cos2t+sin2t+cosht+sinht+3sint-3t…

Q: Evaluate the integral cos"() sin(x) dæ cos'4 using the substitution u = 1 = cos(x). | cos"(x) sin(x)…

A:

Q: Evaluate the integral. sin (8t + 16) dt cos (8t + 16) sin (8t + 16) dt = cos (8t + 16)

A: Solved below

Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: /2 cos x -dx- 1+(sin x)? Compute the integral

A: Consider the following definite integral: ∫0π2cosx1+sinx2dx Substitute sinx=u→cosxdx=du in the above…

Q: Evaluate the integral. 3y- cos xy dy dx x/3 O 5(1 - cos 3) O 3(1 - cos 3) O cos 3 -1 (1 cos 3)

A: Given: ∫03∫x313y2 cos xy dy dx We have x3≤y≤1 and 0≤x≤3 This can be seen as: We can change the…

Q: Evaluate the integral ∫sin (2t + 1)/cos2 (2t + 1) dt

A: Given information: ∫sin2t+1cos22t+1dt

Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: 7. Use integration by parts to prove that for any positive integer n, п - 1 Scos | cos"x dx = 1…

A:

Q: The suitable substitution to evaluate the integral cos°(2x) dx is 5(2x) 3 csc°(2x) u = sin(2x) u =…

A: First, simplify the integrand and use the substitution method

Q: Q4: a)Evaluate the integral: ( In(cosh2x) coth2x dx b) prove that sec-1x = cos-1! = Cos

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Q: 7) Evaluate the indefinite integral / cos cos 2t sin 2t dt.

A:

Q: Integr S√₂-cod -1 ation fuctions. 1-cos²x) dx Not of the above B 1 O

A:

Q: Evaluate the definite integral: 2 1 de sin 0 + cos 0 +1

A:

Q: 1. Evaluate the integral 7/2 cos xesinx *dx

A:

Q: the integral of tan^2 (x) cos^3 (x)dx

A: To evaluate the given trigonometric integral

Q: Evaluate the integral. S sin (7x - 10) dx ㅇ cos (7x-10) +C -cos (7x - 10) + C cos (7x - 10) + C 7…

A:

Q: What is the integrable form of sin 0 sin-cos-sine d@? 2 2 u² – 1 du 1– u² du 2 | cosu du -2 | sinu…

A:

Q: Evaluate the integral. dx JSlx2 - 3 sin 1 33 x + C 3 sec1 |9x - 3| + C sec 1 19 x| +C * sec 13/5 x|…

A:

Q: Evaluate the integral cos3 x + sin² x + 1 dx cos² x (sin2 x + 1)

A:

Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3xbecomes v uz du. -9/29 Select…

A: Given,

Q: Evaluate integral 0 to pie sin 2 x cos 3 x dx

A: Explanation: Given that,  ∫0πsin2xcos3xdx   Formula Used: Trig. identity:1-sin2x=cos2xSum rule of…