use the fundamental theorem to evaluate each integral?

Question

a) the integral from 2 to 5 of [(x-3)(3x+5)]dx

b) the integral from 0 to pi/3 of [(1/sin x)/(cos ^2x)]dx

c) the integral from pi/4 to pi/3 of [csc t(csc t-2cot t)]dt

d) the integral from ln 3 to 3ln3 of [e^x]dx

pleasee show as much work as possible for any of these i am veryy confused! thanksss!

Answer 1

a)(x-3)(3x+5)=(3x^2-4x-15)
integ (3x^2-4x-15)= 3x^3/3-4x^2/2-15x
=x^3-2x^2-15x
when x=5, 5^3-2(5^2)-15(5)=125-50-75=0
when x=2, 2^3-2(2^2)-15(2)=8-8-30
0-(-30)=30

b) csc^2(t) -2csc(t)cot(t)
integrating,
-cot(t)+2d(csc(t))
=-cot(t)-2csc(t)
evaluate from pi/4 and pi/3 and subtract

c)integ of e^x is e^x
e^3ln(3) - e^3
e^ln(27) - e^3
27-e^3