= Consider the integral f sin-¹x dx. If we let u = sin¯¹x and dv dx, the integral. can be written as xsin¯¹x + ƒ ƒ(x) dx. If we let f f(x) dx = F(x) + C, what is the value of F(1/2) - F(0)? A) O √3-2 B 2 © √³ +1 √3-4 2

Q: The first derivative of y = cos(3x-8) is O a. - sin( 3x-8) O b. 3 sin( 3x-8) O. - 3xsin( 3x-8) O d.…

A: Given function is, y=cos3x-8.   It is differentiated as follows: dydx=ddxcos3x-8

Q: Show that J (x) = 2 sin x

A: By definition,                  . Now,  we need to prove the above statement by taking n = 1/2.

Q: Determine 3 sec(9x) tan (9x) dx

A: We have to determine the value of integral: ∫3 sec 9x tan 9x dx Solving given indefinite integral by…

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

A:

Q: Evaluate sin dx

A:

Q: -1x) dx

A:

Q: sin 3x dx 3-10cos3x 10.

A:

Q: , 8 tan² (2x) dx

A:

Q: Evaluate ∫ 3x2 sin(x3) dx.

A: To evaluate the integral  ∫3x2 sinx3 dx

Q: Find f. f"(x)  =6 x + Sin x

A: Given: f"x=6x+sinx we know that f'x=∫f"xdx                                      ..1 so, by using…

Q: Find a suitable substitution for evaluating ∫tan x sec2 x dx andexplain your choice.

A: we have to integrate the following integral using a suitable substitution. ∫tanx.sec2xdx

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

A: