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
\(\frac{1}{3}\)
\(\frac{2}{3}\)
\(\frac{4}{3}\)