Question
Evaluate the following integrals. Show all the steps in your calculation.
a. ç_0^2(3x^3 - x^2 + 2)dx
b. ç_0^1(e^2x - x^2)dx
c. ç1/(x+3)dx
a. ç_0^2(3x^3 - x^2 + 2)dx
b. ç_0^1(e^2x - x^2)dx
c. ç1/(x+3)dx
Answers
Hy'le
Evaluate the following integrals. Show all the steps in your calculation.
a. ç_0^2(3x^3 - x^2 + 2)dx
b. ç_0^1(e^2x - x^2)dx
c. ç1/(x+3)dx
a. ç_0^2(3x^3 - x^2 + 2)dx
b. ç_0^1(e^2x - x^2)dx
c. ç1/(x+3)dx
Steve
a. This just a simple power rule:
∫x^n dx = 1/(n+1) x^(n+1)
b. same here, also
∫e^u du = e^u
Let u=2x so du = 2 dx
c. Recall that ∫ 1/u du = ln(u)
Let u = x+3
Don't forget the +C on indefinite integrals
∫x^n dx = 1/(n+1) x^(n+1)
b. same here, also
∫e^u du = e^u
Let u=2x so du = 2 dx
c. Recall that ∫ 1/u du = ln(u)
Let u = x+3
Don't forget the +C on indefinite integrals