# Find \int_0^8 (2f(x)-3g(x))dx if \int _0^3 f(x)dx=17, \int_3^8 f(x)dx=-15, and \int_0^8 g(x)dx=12

## Question:

Find {eq}\int_0^8 (2f(x)-3g(x))dx{/eq} if {eq}\int _0^3 f(x)dx=17, \int_3^8 f(x)dx=-15{/eq}, and {eq}\int_0^8 g(x)dx=12{/eq}

## The Fundamental Theorem of Calculus

If a function has a defined antiderivative, we can use the Fundamental Theorem of Calculus to find a numerical result for a definite integral by using the below statement.

{eq}\int_a^b f(x) dx = F(b) - F(a) {/eq}

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When integrating a sum or difference of functions, we can integrate term by term. We can also pull out coefficients. Thus, we can rewrite our integral...

The Fundamental Theorem of Calculus

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Chapter 12 / Lesson 10
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The fundamental theorem of calculus links derivatives and antiderivatives in order to find the area under a curve. Learn more about the theorem with an example using velocity.