Integrals calculus

Question

Answer 1

a) we know this integral evaluates to 2. The constant 3 is factored out and multiplied to the integral result (2) which gives us 3 * 2 = 6 as the answer.

b) splitting this integral into two integrals gives us one integral (f(theta)) which evaluates to 2 multiply this by the constant 4 which returns 8. The second integral (g(theta)) evaluates to -3 multiplied by the constant -3 which returns -9. 8 - (-9) = 17 as the answer

c) the integral of (g(t))^2 = 5 and the integral of (f(t))^2 = 10. Their difference is thus 5 - 10 = -5

d) the integral of (g(x))^2 = 5 and the integral of g(x) = -3. Squaring the integral of g(x) is equivalent to (-3)^2 = 9. Thus we have 5 - 9 = -4 as the answer.

I hope that helps

Answer 2

a) =3 x2 = 6

b) = 4x2 -(3)(-3) = 8+9=17

c) = 10-5 = 5

d)= 10-9= 1

e)