Q. 37 Complete example 2 by evaluating... [FREE SOLUTION]

Chapter 9: Q. 37 (page 756)

Complete example 2 by evaluating the integral expression
${鈭�}_{0}^{\frac{2 蟺}{3}} {(\frac{1}{2} + \cos 胃)}^{2} d 胃 - {鈭�}_{蟺}^{\frac{4 蟺}{3}} {(\frac{1}{2} + \cos 胃)}^{2} d 胃$

Short Answer

Expert verified

The value of the integral is 2.08

Step by step solution

Given information

We are given an integral ${鈭�}_{0}^{\frac{2 蟺}{3}} {(\frac{1}{2} + \cos 胃)}^{2} d 胃 - {鈭�}_{蟺}^{\frac{4 蟺}{3}} {(\frac{1}{2} + \cos 胃)}^{2} d 胃$

Evaluate

We have,

${鈭�}_{0}^{\frac{2 蟺}{3}} {(\frac{1}{2} + \cos 胃)}^{2} d 胃 - {鈭�}_{蟺}^{\frac{4 蟺}{3}} {(\frac{1}{2} + \cos 胃)}^{2} d 胃 = {鈭�}_{0}^{\frac{2 蟺}{3}} (\frac{1}{4} + \cos 胃 + \cos^{2} 胃) d 胃 - {鈭�}_{蟺}^{\frac{4 蟺}{3}} (\frac{1}{4} + \cos 胃 + \cos^{2} 胃) d 胃 = {[\frac{1}{4} 胃 + \sin 胃 + \frac{1}{2} 胃 + \frac{\sin 2 胃}{4}]}^{\frac{2 蟺}{3}}_{0} - {[\frac{1}{4} 胃 + \sin 胃 + \frac{1}{2} 胃 + \frac{\sin 2 胃}{4}]}^{\frac{4 蟺}{3}}_{蟺} = 2.22 - 0.1358 = 2.08$

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Complete example 2 by evaluating the integral expression
${鈭�}_{0}^{\frac{2 蟺}{3}} {(\frac{1}{2} + \cos 胃)}^{2} d 胃 - {鈭�}_{蟺}^{\frac{4 蟺}{3}} {(\frac{1}{2} + \cos 胃)}^{2} d 胃$

Short Answer

Step by step solution

Given information

Evaluate

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Complete example 2 by evaluating the integral expression鈭�02蟺3(12+cos胃)2d胃-鈭�蟺4蟺3(12+cos胃)2d胃

Short Answer

Step by step solution

Given information

Evaluate

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Complete example 2 by evaluating the integral expression
${鈭�}_{0}^{\frac{2 蟺}{3}} {(\frac{1}{2} + \cos 胃)}^{2} d 胃 - {鈭�}_{蟺}^{\frac{4 蟺}{3}} {(\frac{1}{2} + \cos 胃)}^{2} d 胃$