Question

Evaluate the following definite integrals:

(a) {-1}^{2}(-3 x^{2}+6 x+2 d x
(b) {1}^{9}√ {x} d x

Answer 1

To evaluate the given definite integrals, follow the steps provided for each part.

Step-by-step explanation:

To evaluate the definite integrals:

(a) ∫-¹₂(-3x² + 6x + 2) dx

(b) ∫¹₉√x dx

In part (a), we integrate term by term. Start by integrating -3x², which becomes -x³. Integrate 6x, which becomes 3x². And integrate 2, which becomes 2x. Then evaluate the antiderivative at the upper bound and the lower bound, and subtract the results.

In part (b), √x is the same as x^(1/2). So we integrate x^(1/2), which becomes (2/3)x^(3/2). Again, evaluate the antiderivative at the upper bound and the lower bound, and subtract the results.