List of top Mathematics Questions on integral asked in CBSE CLASS XII

Using integration, find the area bounded by the ellipse \( 9x^2 + 25y^2 = 225 \), the lines \( x = -2, x = 2 \), and the X-axis.

Determine the number of units (\( x \)) that should be sold to maximise the revenue \( R(x) = x \cdot p(x) \). Also verify the result.

Sketch the graph of \( y = x|x| \) and hence find the area bounded by this curve, the X-axis, and the ordinates \( x = -2 \) and \( x = 2 \), using integration.

Find: \[ \int \frac{3x+5}{\sqrt{x^2+2x+4}} \,dx. \]

Find: \[ \int e^x \left[ \frac{1}{(1+x^2)^{3/2}} + \frac{x}{\sqrt{1+x^2}} \right] dx. \]

Evaluate \( \int \frac{dx}{x(x^2-1)} \).