(2) Prove that for any integer L () NTX / sin? dx = L. L -L

Q: Simpliyn² + n to got

A:

Q: The function re* sin(8x) is annihilated by the operator

A:

Q: If I, = [x^tan"x dx, Prove that (n+1), + (n-1),,2 ° п 1 %3D 2 n

A:

Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: +¹²+z111² Prove that x12 where prime denotes differentiation w.rts. = 1 p² o² + 1+p¹² P

A:

Q: Evaluate sin dx

A:

Q: -1x) dx

A:

Q: prove 2sin-1 (3/5)=tan-1(24/7)

A:

Q: Evaluate p* sin 0 de dr.

A:

Q: Evaluate d/dx { In√(x+1)}

A:

Q: , 8 tan² (2x) dx

A:

Q: 2n2 Using the mean-value theorems, show that in sin z w/6

A:

Q: Find sin a. (-/5 ,2) [ ?] 1

A:

Q: 11:2 +¸µ¹¹:¹² + z ¹¹12 Prove that x12 denote differentiation w.r.t.s. = 1 p² 0² + 1+p²². 04 11 1 R²…

A:

Q: * lif z= 4i / (-3-4i) , find |z

A:

Q: lim, 0 6 tan² (5x) 15x²

A:

Q: Evaluate lim i+ cos rj sin (at)

A: Follow the procedure given below.

Q: If secA=x+1/4x ,prove that secA+tanA=2x or 1/2x

A:

Q: Show that cosh x> 1 + x² for all x.

A: comparison

Q: Determine 1-/[e-tt sin(2t)] 2- 23+3s)*

A: Given

Q: 2) Evaluate: 6+ 1-x² i) dx

A: