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Solve pls ∫tan -1 (1-x+x 2 ) dx Limit if from 0 to 1.

Solve pls
∫tan-1(1-x+x2) dx
Limit if from 0 to 1.

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int_{0}^{1}tan^{-1}(1-x+x^2)dx
I = \int_{0}^{1}cot^{-1}(\frac{1}{1-x+x^2})dx
I = \int_{0}^{1}cot^{-1}(\frac{1}{1-x(1-x)})dx
I = \int_{0}^{1}(\frac{\pi }{2}-tan^{-1}(\frac{1}{1-x(1-x)}))dx
I = \int_{0}^{1}(\frac{\pi }{2}-(tan^{-1}x-tan^{-1}(1-x))dx
I = \int_{0}^{1}\frac{\pi }{2}dx-\int_{0}^{1}tan^{-1}xdx+\int_{0}^{1}tan^{-1}(1-x)dx
I = \int_{0}^{1}\frac{\pi }{2}dx-\int_{0}^{1}tan^{-1}xdx+\int_{0}^{1}tan^{-1}(1-(1-x))dx
I = \int_{0}^{1}\frac{\pi }{2}dx-\int_{0}^{1}tan^{-1}xdx+\int_{0}^{1}tan^{-1}xdx
I = \frac{\pi }{2}

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