Applications of Integrals

Find the area of the region bounded by the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$.

Find the area of the region bounded by the ellipse $\frac{x^2}{4} + \frac{y^2}{9} = 1$.

Area lying in the first quadrant and bounded by the circle $x^2 + y^2 = 4$ and the lines $x = 0$ and $x = 2$ is

Area of the region bounded by the curve $y^2 = 4x$, $y$-axis and the line $y = 3$ is

Find the area under the given curves and given lines:

Sketch the graph of $y = |x + 3|$ and evaluate $\int_{-6}^{0}|x + 3|dx$.

Find the area bounded by the curve $y = \sin x$ between $x = 0$ and $x = 2\pi$.

Area bounded by the curve $y = x^3$, the $x$-axis and the ordinates $x = -2$ and $x = 1$ is

The area bounded by the curve $y = x|x|$, $x$-axis and the ordinates $x = -1$ and $x = 1$ is given by