List of top Mathematics Questions on Area under Simple Curves asked in JEE Main

The area of the region \(\left\{(x,y):x^2≤y≤|x^2-4|,y≥1\right\}\) is 
The number of points, where the curve y = x5 – 20x3 + 50x + 2 crosses the x-axis, is _____.
If the solution curve of the differential equation \(\frac{dy}{dx} = \frac{x + y - 2}{x - y}\) passes through the points \((2, 1)\) and (k + 1, 2), k > 0, then
If the tangent to the curve y = x3 – x2 + x at the point (a, b) is also tangent to the curve y = 5x2 + 2x – 25 at the point (2, –1), then |2a + 9b| is equal to _____ .
The area of the region 
\(\begin{array}{l} \left\{\left(x,y\right);\left|x-1\right|\leq y \leq \sqrt{5-x^2} \right\}\end{array}\)
is equal to
The odd natural number a, such that the area of the region bounded by \(y = 1, y = 3, x = 0, x = y^a\) is \(\frac {364}{3}\), is equal to

Let a triangle ABC be inscribed in the circle
\(x² - \sqrt2(x+y)+y² = 0\)
such that ∠BAC= π/2. If the length of side AB is √2, then the area of the ΔABC is equal to :

The area enclosed by the curves 
\(\begin{array}{l} y=\text{log}_e\left(x+e^2\right),\ x=\text{log}_e\left(\frac{2}{y}\right)\text{ and }x=\text{ log }_e\ 2,\end{array}\)
above the line y = 1 is
The area bounded by y = min{sin x, cos x} and x-axis in -π ≤ x ≤ π interval is equal to (in sq. units):
Find area bounded by $y^2 ≤ 2x$ and $y ≥ 4x – 1$