List of top Mathematics Questions on Application of Integrals asked in JEE Main

The area of the region bounded by the curves \(x + 3y^2 = 0\) and \(x + 4y^2 = 1\) is equal to:

If the area of the region bounded by \(16x^2 - 9y^2 = 144\) and \(8x - 3y = 24\) is \(A\), then \(3(A + 6 \log_e(3))\) is equal to _______.

The area of the region \(\{(x, y): y \le \pi - |x|, y \le |x \sin x|, y \ge 0\}\) is:

The area bounded by \[ 2 - 4x \leq y \leq x^2 + 4 \quad \text{and} \quad x = \frac{1}{2}, \, x \geq 0, \, y \geq 0 \] (in square units) is:

The area of the region, inside the ellipse \(x^2+4y^2=4\) and outside the region bounded by the curves \(y=x-1\) and \(y=1-x\), is:

If the area of the region \( \{ (x, y) : x^2 + 1 \leq y \leq 3 - x \} \) is divided by the line \( x = -1 \) in the ratio \( m : n \) (where \( m \) and \( n \) are coprime natural numbers), then the value of \( m + n \) is:

Area enclosed by \[ x^2 + 4y^2 \leq 4, \quad |x| \leq 1, \quad y \geq 1 - |x| \text{ is} \]