Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

Solve the differential equation \[\left( y + 3 x^2 \right)\frac{dx}{dy} = x\]

Find the particular solution of the differential equation \[\frac{dx}{dy} + x \cot y = 2y + y^2 \cot y, y ≠ 0\] given that x = 0 when \[y = \frac{\pi}{2}\].

Solve the following differential equation:- \[\left( \cot^{- 1} y + x \right) dy = \left( 1 + y^2 \right) dx\]

Write a value of

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Write a value of\[\int \cos^4 x \text{ sin x dx }\]

Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]

Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]

Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].

Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]

Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]

Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]

Write a value of\[\int \log_e x\ dx\].