Evaluate the definite integral. Use a graphing utility to verify your result. \int_{-5}^{5}...

Question:

Evaluate the definite integral. Use a graphing utility to verify your result.

{eq}\displaystyle \int_{-5}^{5} (t^2-4) \, dt {/eq}

Power Rule:

To integrate a power function, recall that {eq}\displaystyle \int t^n \, dt = \frac{t^{n+1}}{n+1} + C {/eq}. The Fundamental Theorem of Calculus states that if {eq}F {/eq} is an antiderivative of {eq}f {/eq}, then {eq}\displaystyle \int_a^b f(t) \, dt = F(b)-F(a). {/eq}

Answer and Explanation: 1

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Integrate the function.

{eq}\displaystyle \int_{-5}^5 (t^2 - 4) \, dt = \frac13 t^3 - 4t \bigg|_{-5}^5 = \bigg(\frac{125}{3}-20 \bigg) - \bigg(-...

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The Fundamental Theorem of Calculus

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Chapter 12 / Lesson 10
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The fundamental theorem of calculus is one of the most important points to understand in mathematics. Learn to define the formula of the fundamental theorem of calculus and explore examples of it put into practice.


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