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Chapter 4: Q. 31 (page 373)

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

鈭�鈭�蟺蟺鈥�(1+sin鈦�x)dx

Short Answer

Expert verified

Ans: The exact value of鈭�鈭�蟺蟺鈥�(1+sin鈦�x)dx=2蟺

Step by step solution

01

Step 1. Given information.

given,

鈭�鈭�蟺蟺鈥�(1+sin鈦�x)dx

02

Step 2. The objective is to determine the exact value of the definite integral. 

The exact value is calculated as shown below,

鈭�-蟺蟺鈥�(1+sin鈦�x)dx=鈭�-蟺蟺鈥�(1)dx+鈭�-蟺蟺鈥�(sin鈦�x)dx=[x]-蟺蟺+[鈭�cos鈦�x]-蟺蟺=蟺+蟺鈭�cos鈦�蟺+cos鈦�(鈭�蟺)=2蟺+0=2蟺

Therefore, the exact value is, 2蟺.

03

Step 3. Check the answer using a graph.

The required graph is,

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