Evaluate the Integral Below:

Question

Evaluate the Integral. please show all steps.

Answer 1

See the video.

Answer 2

If f(x) = 4x² + x + 2, then an antiderivative (without the constant) is found by raising each exponent by 1, and multiplying by the reciprocal of the new exponent--or equivalently dividing by the new exponent--term by term.

F(x) = (4/3)x³ + (1/2)x² + 2x

To evaluate the definite integral determine F(2) - F(1).

[((4/3)(2)³ + (1/2)(2)² + 2(2) ) - (4/3 + 1/2 + 2)]

[(32/3 + 2 + 4) - (4/3 + 1/2 + 2)]

[(64/6 + 36/6) - (8/6 + 3/6 + 12/6)]

[(100/6) - (23/6)]

77/6

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