NCERT Solutions
Class 12 - Mathematics Part-2 - Chapter 8: APPLICATION OF INTEGRALS
Miscellaneous Exercise on Chapter 8

Question. 1

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

(A)

\(-9\)

(B)

\(-\frac{15}{4}\)

(C)

\(\frac{15}{4}\)

(D)

\(\frac{17}{4}\)

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

(A)

(B)

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

(C)

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

(D)

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