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Chapter 5: Q. 53 (page 496)

${鈭�}_{0}^{8} x^{- 1 / 3} d x$

Short Answer

Expert verified

${鈭�}_{0}^{8} x^{- 1 / 3} d x = 6$

Step by step solution

Given information

${鈭�}_{0}^{8} x^{- 1 / 3} d x$

Calculate integral

As we know that,

$鈭� x^{n} d x = \frac{x^{n + 1}}{n + 1} + C, Where C is a constant$

By using the above formula,

${鈭�}_{0}^{8} x^{- 1 / 3} d x = {[\frac{x^{- 1 / 3 + 1}}{- \frac{1}{3} + 1}]}_{0}^{8} 鈬� = \frac{3}{2} {[x^{2 / 3}]}_{0}^{8} 鈬� = \frac{3}{2} (8^{2 / 3}) 鈬� = \frac{3}{2} 脳 4 鈬� = 6$

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Most popular questions from this chapter

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Problem Zero: Read the section and make your own summary of the material.

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鈭�08x-1/3dx

Short Answer

Step by step solution

Given information

Calculate integral

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${鈭�}_{0}^{8} x^{- 1 / 3} d x$