n 4i 5) What definite integral is represented by lim 2 ? Use the Fundamental Theorem to n-00 i = 1 evaluate the integral. 1 4 B) 4 4 4x2 dx = 64 x2 dx 3 x2 dx = 21 A) C) x dx = 64 D) 3

Q: Evaluate the integral. *1/3 3 sec 0 tan 0 de IT/4

A: Given ∫π/4π/33 sec θ tan θ dθWe know that ∫sec(x)tan(x)dx=sec(x)Therefore ∫3 sec θ tan θ dθ=3sec θ+C

Q: 6 2" – 5 sin(r) + dx 1+x?

A:

Q: Steps

A:

Q: Evaluate the indefinite integral. Sa V1 - a? dæ cos° 0 – cos 0 +C 3 - 5/2 (1-22)이2-3 (1- 22)이2 +C. |…

A:

Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

Q: 12 Evaluate 1²√√36 - (x - 6)² dx using area formulas.

A: We have to evaluate the given integration.

Q: Use an appropriate choice of contour integrals in the complex plane to show that the integral (along…

A: To evaluate the integral ∫−∞∞​x3−i1​dx using contour integration, we will use the residue theorem.…

Q: 1) Evaluate. x cosh ax dx

A: As per guideline we have to solve one question

Q: 23) 8 e-5x dx e5x

A:

Q: (d) Derive the formula cosh-¹(x) = ± In (x + √x² - 1)

A: