Chapter 4: Q. 47 (page 353)

Calculate the exact value of each definite integral in Exercises 47–52 by using properties of definite integrals and the formulas in Theorem 4.13.
$\int_{2}^{4} (x^{2} + 1) d x$

Short Answer

Expert verified

The exact value of definite integral is $\frac{62}{3}$ .

Step by step solution

Step 1. Given Information

We are given,

$\int_{2}^{4} (x^{2} + 1) d x$

Step 2. Finding the Integral

The definite integral is given by,

$\int_{2}^{4} (x^{2} + 1) d x = \int_{2}^{4} x^{2} d x + \int_{2}^{4} 1 d x = \frac{1}{3} [4^{3} - 2^{3}] + 1 [4 - 2] = \frac{1}{3} [64 - 8] + 2 = \frac{56}{3} + 2 = \frac{62}{3}$

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Calculate the exact value of each definite integral in Exercises 47–52 by using properties of definite integrals and the formulas in Theorem 4.13.
$\int_{2}^{4} (x^{2} + 1) d x$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the Integral

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Calculate the exact value of each definite integral in Exercises 47–52 by using properties of definite integrals and the formulas in Theorem 4.13.∫24x2+1dx

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the Integral

One App. One Place for Learning.

Most popular questions from this chapter

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Calculate the exact value of each definite integral in Exercises 47–52 by using properties of definite integrals and the formulas in Theorem 4.13.
$\int_{2}^{4} (x^{2} + 1) d x$