Q. 4 TB - Calculus

Question

Approximating definite integrals: Use a calculator or computer algebra system to approximate the values of the following definite integrals.

$$\begin{gathered} {\int }_{-1}^3\sqrt{1+e^{2x}}dx \\ {\int }_0^{2\pi }\sqrt{1+{\sin }^{2}x}dx \end{gathered}$$

Step-by-Step Solution

Answer

The values of the given definite integrals are 20.7205099539 and 7.64039557806.

Step 1: Given

The given definite integrals are:

$$\begin{gathered} {\int }_{-1}^3\sqrt{1+e^{2x}}dx \\ {\int }_0^{2\pi }\sqrt{1+{\sin }^{2}x}dx \end{gathered}$$

Step 2: To find

Use a calculator or computer algebra system to approximate the values of the following definite integrals.

Step 3: Calculation

Using a calculator we get: 

$$\begin{gathered} {\int }_{-1}^3\sqrt{1+e^{2x}}dx=20.7205099539 \\ {\int }_0^{2\pi }\sqrt{1+{\sin }^{2}x}dx=7.64039557806 \end{gathered}$$