Calculus Question

Question

a) If F(x) = x³ - 4x² -5x then ∫₁² blank dx = blank

b) If F(x) = e^x + 3x then ∫⁵₃ blank dx = blank

Answer 1

a) F(x)= x^3-4x^2-5x= integral of F'(x)dx=f(x)dx

=(3x^2-4x-5) dx

evaluated from 1 to 2 = 12-8-5 -(3-4-5)=-1+6=5

b) F(x)= e^x+3x = integral of F'(x)dx= f(x)dx = (e^x +3)dx evaluated from 3 to 5=e^5 -e^3 = about 128.33