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Chapter 4: Q. 48 (page 353)

Calculate the exact value of each definite integral in Exercises 47鈥�52 by using properties of definite integrals and the formulas in Theorem 4.13.
${鈭�}_{0}^{6} (3 x + 2) d x$

Short Answer

Expert verified

The exact value of definite integral is $66$ .

Step by step solution

01

Step 1. Given Information

We are given,

${鈭�}_{0}^{6} (3 x + 2) d x$

02

Step 2. Finding the Integral

The definite integral is given by,

${鈭�}_{0}^{6} (3 x + 2) d x = {鈭�}_{0}^{6} 3 x d x + {鈭�}_{0}^{6} 2 d x = 3 {(\frac{x^{2}}{2})}_{0}^{6} + 2 (x)_{0}^{6} = 3 (\frac{1}{2} (6^{2})) + 2 (6 - 0) = 54 + 12 = 66$

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Most popular questions from this chapter

If ${鈭�}_{- 2}^{3} f (x) d x = 4, {鈭�}_{- 2}^{6} f (x) d x = 9, {鈭�}_{- 2}^{3} g (x) d x = 2$ , and ${鈭�}_{3}^{6} g (x) d x = 3$ , then find the values of each definite integral in Exercises $29 - 40$ . If there is not enough information, explain why.

${鈭�}_{- 2}^{- 2} x (f (x) + 3)^{2} d x$

Write out all the integration formulas and rules that we know at this point.

Given a simple proof that ${鈭�}_{k = 5}^{n} (a_{k} + b_{k}) = {鈭�}_{k = 5}^{n} a_{k} + {鈭�}_{k = 5}^{n} b_{k}$

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.

${鈭�}_{0}^{蟺} 鈥� (\sin^{2} 鈦� x + \cos^{2} 鈦� x) d x$

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.

${鈭�}_{0}^{1} 鈥� \frac{1}{2 e^{x}} d x$

See all solutions

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