12. Find L (e" sin 2t)

Q: d) sin (x)e3*+ dx dx

A: The given integral is definite integral because limits are given.  So integration value will be a…

Q: Solve Sx Joox Sx Jox) Sin (x) dx

A: We can solve the integral using integration by parts: Let u = Jo(x), and dv = sin(x) dx, then dudx =…

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: dx sin x cos x

A:

Q: d [sin? (In x)] dx

A:

Q: 11. Find e*sinx dx

A:

Q: 59. Find (a) {e-t sin? t},

A: Let's find.

Q: 2. S2² 52. x² sin 2x dx

A:

Q: Find [(x- sin(2x)) dx

A:

Q: 4. Solve sin (2-) = 1.

A:

Q: sin(3x)e°*dx

A:

Q: 2x fe²x sinx dx

A: Using integration by part.

Q: sin 5 (17x) dx = [

A: To evaluate : ∫sin517xdx Let I = ∫sin517xdx ⇒I =∫sin417xsin(17x) dx

Q: A ( sinh x- coshx tanh e 6)

A: You all need to have the idea of hyperbolic and their basic calculus.

Q: 2. Find [cot (x)sin* (x)dx

A: First simplify then integrate

Q: sin(In x) dx

A:

Q: solve for y'. y=sin-1[(ax+b)/(bx+a)]

A: Sin-1x can be written as asin(X)   So we have expression as y=sin-1(ax+b)(bx+a) We have to solve for…

Q: S (|sin x| + sin æ') dx

A:

Q: 1. /2х— х2 dx

A: Given ∫2x-x2 dx The given term can be rewritten as ∫2x-x2 dx= ∫2x-x2-12+12 dx so we get…

Q: 1. L 16x dx 2. o &. + 2 +1 3. (sec x- tan x dx dx 4. cos x tan x 1/4

A:

Q: d. f(x)= sin (1-x)

A:

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

A: To evaluate the given integrals by substitution.

Q: Evaluate : e2x sin3x dx

A: Introduction :

Q: sin“ (x)dx 4

A:

Q: 3. √9-x2 dx (hint: sin x = S dx (hint: sinx = (sin²x)(sin²x)) x4

A:

Q: sin-'x - cos-1x = " Find the value of x

A: Given that sin-1 (x)-cos-1 (x)=π6, Our Aim is to find the value of x=?

Q: Which of the expressions below are equivalent? Which are not? Explain. i. sin '(x) ii. csc(x) iii.…

A: It is known that sin-1x can also be written as arcsinx.

Q: cos² (In x) sin²(In x)

A: Given: I=∫cos2(lnx)sin2(lnx)xdx

Q: 7. fex tan¹(ex dx

A:

Q: b) Evaluate S e-2t sinht dt an

A: