Evaluate Definite Integral Calculus 101: 3x^2 + 4x - 5 from 1 to 2

Published on April 21, 2026

Calculus

Solve the definite integral of 3x^2 + 4x - 5 with respect to x from 1 to 2 using the Fundamental Theorem of Calculus.

Question

Answer

The problem asks us to evaluate the definite integral:

To evaluate this definite integral, we first find the antiderivative of the integrand

.
Using the power rule for integration, which states that

(where

), we can find the antiderivative of each term:
The antiderivative of

.
The antiderivative of

So, the antiderivative of

Now, we use the Fundamental Theorem of Calculus to evaluate the definite integral. The theorem states that

, where

is the antiderivative of

In this case,

and

.
We need to calculate

First, evaluate

Next, evaluate

Finally, subtract

from

The final answer is

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