Let F(x) = | t tan(t) dt 7/4 Find F(T/4) F'(T/4) F"(T/4). Express your answer as a fraction. You must show your work. a. b. С.

Q: ind the derivative. FA h Cx) = 2. (5x*+4

A: To find  The derivative of h(x)

Q: Evaluate 3 | ((2 – 1)32, (3 + t)2, 1)dx. 3/2 3/2 -3

A:

Q: B- Find dy / dx for the following functions: (3 mark) * 1- Y= sin( coshx log, 2 )

A:

Q: d -[x*] = xx"-1 dx

A:

Q: Find f. f"'(t)  = t   - √t

A: To find f"(t) we integrate f"'(t)

Q: 5. Change of variable 2 x dx 3x+1 a.

A: Given function, ∫12x3x+1dx

Q: dx 2(x - 2)²

A: To evaluate,∫1x2x-22dx

Q: find dy. y =2√x/3(1 + √x)

A: we have to find the derivative y=2x3(1+x)

Q: O Find (a) |VT-x)/x dx, (c) (4-x*y² dx. Ans, ía) 1/60, (/) x/2. (c) 31

A:

Q: dx d. de. f(3x + 2)5 dx f sec²x

A:

Q: (cosh ar +h)dr

A:

Q: Evaluate Set 7x cos (6x) dx. Sex cos (6x) dx =

A:

Q: 1. 2 sec" (8x -) d n) dx

A: to evaluate the integration of 2sec^2(8x-π/4)

Q: dr Find if r (x) = 9x 2 + 5x – 3. dx

A: Given,            r(x) = 9x2 + 5x - 3

Q: . Evaluate 4 x³. Cot-1x dx

A: Please go through the attached solution.  Thankyou . Best regards.

Q: Calculate the following integrals a) S .3 dx;u = x³ – 1 | Vx3-1 3x b) S dx; u = e3x +1 e3x +1 c) S *…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 4. Evaluate f(2-x)/x dx.

A: To find the given integral open the bracket and split the given integral in to two integrals.

Q: Q.2: Evaluate: -2 2 dx 1 I = x2 - 8.

A: