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

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Grade 12Integral Calculus

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

Lovey

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below

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