6 Evaluate the following indefinite integrals. a) f(xx²- csex.cot x) dx 3 S(√x³+√³x² - 10) dx X 4) c) 3 cos²x dx e applying This

Q: J X √9 - x² dx

A:

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: Evaluate S₁ 45 dx 1- cos (9x)

A: To evaluate .

Q: Evaluate the indefinite integral. / COS X 5 sin x + 15 dx

A: This question is about integral calculus.

Q: Evaluate f x² cos 4x dx Evaluateſ sin* 3x cos3 3x dx Evaluate the integral J x²+x-1 dx x(x²-1)

A: Given:   i) ∫x2cos 4x dx      integrate by parts ∫fg'=fg-∫f'g     here f=x2,f'=2x , g'=cos…

Q: /2 cos x -dx- 1+(sin x)? Compute the integral

A: Consider the following definite integral: ∫0π2cosx1+sinx2dx Substitute sinx=u→cosxdx=du in the above…

Q: (ii) Evaluate the definite integral r³e² dr.

A:

Q: Integrate ing with res pect to x; +8 - (3x+2) - the followi Sin (x) + + 2 4x dx 4 5x

A: Formula : 1. ∫xndx=xn+1n+1, n≠12.∫(ax+b)ndx=(ax+b)n+1a(n+1)3.∫1xdx=lnx4.∫sinx…