Activity 4.4.2

Use the Fundamental Theorem of Calculus to evaluate each of the following integrals exactly. For each, sketch a graph of the integrand on the relevant interval and write one sentence that explains the meaning of the value of the integral in terms of the (net signed) area bounded by the curve.

1. $\int_{-1}^4 (2-2x) \, dx$

2. $\int_{0}^{\frac{\pi}{2}} \sin(x) \, dx$

3. $\int_0^1 e^x \, dx$

4. $\int_{-1}^{1} x^5 \, dx$

5. $\int_0^2 (3x^3 - 2x^2 - e^x) \, dx$