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ans of these two questions and give me full solution of these questions

ans of these two questions
and give me full solution of these questions

Question Image
Grade:12

1 Answers

Atul Singh
28 Points
4 years ago
Question 1)
\int \sqrt{1 + cos2x}
1 can be written as cos^{2}x + sin^{2}x
and cos2x can be written as cos^{2}x - sin^{2}x
Adding both and substituting you get 
\int \sqrt{1 + cos2x}=\int \sqrt{2 cos^{2}x} = \int \sqrt{2} cosx =\sqrt{2}sinx
 
 
Question 2)
\int_{0}^{1}\frac{1}{1+x^{2}}
We know that:
\int\frac{1}{1+x^{2}} = tan^{-1}x

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