Login/Sign Up
Home » Choose the correct option: Area bounded by the curve -axis and the ordinates and is given by [Hint: if and if ] A. 0 B. C. D.
Choose the correct option: Area bounded by the curve ^{y=x|x|}, x-axis and the ordinates x=-1 and x=1 is given by [Hint: y=x^{2} if x>0 and y=-x^{2} if x<0 ]
A. 0
B. ^{\frac{1}{3}}
C. \frac{2}{3}
D. \frac{4}{3}
Applications of Integrals | CBSE | Class 12 | Maths | Miscellaneous | NCERT
Choose the correct option: Area bounded by the curve ^{y=x|x|}, x-axis and the ordinates x=-1 and x=1 is given by [Hint: y=x^{2} if x>0 and y=-x^{2} if x<0 ]
A. 0
B. ^{\frac{1}{3}}
C. \frac{2}{3}
D. \frac{4}{3}

Solution:


\text { Required area }=\int_{-1}^{1} y d x
\begin{array}{l} =\int_{-1}^{1} x|x| d x \\ =\int_{-1}^{0} x^{2} d x+\int_{0}^{1} x^{2} d x \end{array}
\begin{array}{l} =\left[\frac{x^{3}}{3}\right]_{-1}^{0}+\left[\frac{x^{3}}{3}\right]_{0}^{1} \\ =-\left(-\frac{1}{3}\right)+\frac{1}{3} \\ =\frac{2}{3} \text { sq.units } \end{array}
As a result, the correct answer is C.

i

More Material