1. Show that Sº, cos dx COS L m +n L n=m

Q: 3. S sin®2y · /cos2y d|

A:

Q: Si sin“ (3y) cos® (3y) dy 128 2340135 128 780045 O 9.64 x 10 4 O 2.89 x 10 3

A:

Q: Given: [ Scos(cos2x) sin2x dx Find: du O 2cos2x dx O -2sin2x dx -2cos2x dx O 2sin2x dx O O

A: ∫coscos2xsin2xdxLet u=cos2x.So,     du=-2 sin(2x) dx

Q: Solve the fllowing D.E +4y= cos x - sinx 2. CoS X %3D

A:

Q: 4. The area which is inside the circle r = 8 cos e and outside the circle r = 2 cos 8.

A: Introduction: In polar coordinate, the equation of a circle centered at the origin with radius a…

Q: (p² –1)cos[cosh (In r)]dr

A: In this question, we need to find the integral.

Q: 2.) If H (y) = cos y – sin y, find H (0), H (n),H (T), and also show that H. n+ x) = H (n - x) = -H…

A: The solution is given as

Q: 3 cos (x) sin (x) dx = %3D 2 15 O None 6

A: To find the value of given ∫0π23cos2xsin3xdx

Q: S 5 sin(3x)e2cos(3r)dx

A: Solve integral by substitution method:-

Q: 10. 3 J√cos z sin ³ zdz COS

A:

Q: Find: O d: x-6,X-1 dy 3 23=Sin (cos 8x)

A: 1 .y=45x3-6x2+x2-12. y=sin(cos(8x))

Q: 2х —1 The value of| dx is 1+x-x, tan А. 1 В. О С. 1 D. 4

A:

Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3r becomes u du. Select one: a.…

A:

Q: 15. For fe' cos x dx, what is du? cos x e' dx - sin x dx G(e* cos x + e" sin x) + C

A: The given question can be solved as shown in step2.

Q: (/2 x cos" x dx, when n> 1, show that Jo If In п(п - 1)1,-2 — 1 In [Hint: cos" x= cos? x.cos"-2 x…

A:

Q: 3. Find . a. y ( +2r + 10) cos(r)

A: Find the derivatives of the given functions. Use the derivative formulas:…

Q: if y = a sin x Prove a +b CosX a cos + b %3D 2 (atb cosx) 11

A:

Q: 9. dt + 을 = COS t + Answer: s = sin t + 을..

A:

Q: Suppose m and n are constants and m‡ n. 1. Evaluate sin(mx) cos(nx) dx

A: using trigonometric identity

Q: 1 dx x +c, find- dx exactly where c is a constant. 5. If 1+cos x = tan 2 X 3+3 cos 4 n dx tam S c /+…

A: It is given that

Q: 2. Find cos ec (In x) dx . x1+ cot(h x)

A:

Q: (d) lim In(cos r) エ→0

A:

Q: Suppose m and n are constants and m #n. Evaluate sin(mx) cos(nx) dx-

A: To evaluate we first multiply and divide by 2 the given function.  Then use the formula: 2(sin(mx)…

Q: e csc 20 In (ecos 2 ) Ince cos CoS 20 28) Sin2 20 OP

A: Given integral is ∫ecsc2θlnecos2θsin22θdθ since lnex=x, so lnecos2θ=cos2θ The integral becomes…

Q: Evaluate. S cos a In(secz)dr COS D

A:

Q: S 1+cos(3x)dx

A: Given : ∫1+cos3xdx

Q: The integral So (cos(3x))² sin(3x)dx under the change of variable u = cos3x becomes - ov 29 9/29 u?…

A:

Q: Prove that: cos(nx) - cos(na) cos(x) – cos(a) sin(na) sin(a) dx = n neN, a ER - {0}

A: To solve this question take different values of n and calculate LHS and RHS separately.     if…

Q: d (c) (cos(2²) + In(3 – 2æ)) dx

A:

Q: de 6) S 7) S(1 – sin? 3t) cos 3t dt 8) ſ tan (5x) sec?(5x) dx cos? e

A:

Q: 4. sin M= 20 16 30 5. tan L = 6. cos Z = 16

A:

Q: 8) S dx it sinx + cos x a) in (1 + tan =) + c b) In (i - tan £) + c c) - In (1 + tan x) + o 2 d.)…

A:

Q: for 0 (0° < 0 < 2n) in the equation 2sin e cos e - sin e - 2cos 0 + 1 = 0.

A: Given that, 2sinθcosθ-sinθ-2cosθ+1=0. We know that, sinθ=sinα⇒θ=nπ+-1n+α       α∈-π2,-π2…

Q: Find Lt+1)²-e' sin² t + cos(t+1 ++ π)}.

A: Given :

Q: S S som'e dx cos'x

A: Perform integration

Q: 6. S sin*(e³*) cos(e³*) e³× dx

A:

Q: /2 | cos(r)e sin z dx O a. el O b. e sin 1 C. 1—е 1 O d. cos 1

A:

Q: 14. Find dr/de: r= 0 sin 0 + cos 0 а. cos @ b. 0 cos 0 0 sin 0 C. O a O b

A:

Q: 5. Evaluate 1. S, sin(x2) dx

A:

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

A:

Q: 2Tt Prove that a" sinax cos bx dx = 0 0.

A:

Q: 4. Prove that the identity is true. 1- cost e = sin² 0 1+ cos e

A:

Q: 4. S(1 – cos 4u) du 5. S sin x cos x dx

A: 4) Given:        ∫1-cos4udu Apply linearity:    =∫1 du-∫cos4u du     =u-∫cos4u du

Q: 9. Integrate the following: a) S sin? x cosx dx b) "(1 – cos 2x)/2dx

A: (b) The given integration is: ∫0π1-cos2x32dx To find the value of integration.

Q: 2 Recall thal cos-x= arccos x, Find /2 X Sin (cos x) dx. C.

A:

Q: 1 La So cos " dy dæ COS evaluate

A: We are given the Integral: ∫π2π∫0x21xcosyxdy dx=∫π2π1xsinyx×1x0x2 dx=∫π2π1x2sin xdx It cannot be…

Q: 1. Evaluate 9/ COS x (a) (1 – x)e dx (b) ,"™ dx p) A-2 sin r -

A:

Q: 7/2 d sin dx dx COS

A:

Q: d le" cos.x) cOS x dx

A: Given ,  d/dx(ex cosx)  We know that  d/dx(uv) = u'v + uv'  Here ,  u = ex and v = cosx Then ,