Find the area of the region bounded by the ellipse \(\frac{x^2}{16} + \frac{y^2}{9} = 1\).
\(12\pi\)
Find the area of the region bounded by the ellipse \(\frac{x^2}{4} + \frac{y^2}{9} = 1\).
\(6\pi\)
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
\(\pi\)
\(\frac{\pi}{2}\)
\(\frac{\pi}{3}\)
\(\frac{\pi}{4}\)
Area of the region bounded by the curve \(y^2 = 4x\), y-axis and the line \(y = 3\) is
2
\(\frac{9}{4}\)
\(\frac{9}{3}\)
\(\frac{9}{2}\)
Find the area under the given curves and given lines:
(i) \(y = x^2\), \(x = 1\), \(x = 2\) and x-axis
(ii) \(y = x^4\), \(x = 1\), \(x = 5\) and x-axis
(i) \(\frac{7}{3}\)
(ii) \(624.8\)
Sketch the graph of \(y = |x + 3|\) and evaluate \(\int_{-6}^{0} |x + 3|\,dx\).
\(9\)
Find the area bounded by the curve \(y = \sin x\) between \(x = 0\) and \(x = 2\pi\).
\(4\)
Area bounded by the curve \(y = x^3\), the x-axis and the ordinates \(x = -2\) and \(x = 1\) is
\(-9\)
\(-\frac{15}{4}\)
\(\frac{15}{4}\)
\(\frac{17}{4}\)
The area bounded by the curve \(y = x|x|\), x-axis and the ordinates \(x = -1\) and \(x = 1\) is given by
0
\(\frac{1}{3}\)
\(\frac{2}{3}\)
\(\frac{4}{3}\)