Problem 26
\(\iint_{R} y d x d y\) where \(R\) in the region bounded by the parabolas \(y^{2}=4 x\) and \(x^{2}=4 y\), is \(\ldots \ldots\)
Problem 27
\(\iint\left(x^{2}+y^{\|}\right) d x d y\) in the positive quadrant for which \(x+y \leq 1\), is . ......
Problem 28
Aree between the paraboles \(y^{2}=4 x\) and \(x^{2}=4 y\) is \(\ldots \ldots\)
Problem 29
Changing the order of integration in \(\int_{-a}^{a} \int_{0}^{\sqrt{a^{2}-y^{2}}} f(x, y) d x d y=\ldots \ldots \ldots\)
Problem 35
The centroid of the area enclosed by the parabola \(y^{2}=4 x, x\)-axis and its latus-rectum is ......
Problem 36
The moment of inertia of a uniform spherieal ball of mass \(10 \mathrm{gm}\) and radius \(2 \mathrm{~cm}\) about a diameter is
Problem 39
\(\int_{0}^{1} \frac{x-1}{\log x} d x=\ldots . . .\)
Problem 41
Value of \(\int_{0}^{a} \int_{0}^{b} \int_{0}^{c} x^{2} y^{3} z^{2} d x d y d z\) is (a) \(\frac{a b c}{3}\) (b) \(\frac{a^{2} b^{2} c^{2}}{27}\) (c) \(\frac{a^{3} b^{3} \mathrm{c}^{3}}{27}\) (d) \(\frac{a^{2} b^{2} c^{2}}{9}\).
Problem 42
The integral \(\int_{0}^{1} \int_{0}^{\sqrt{1-x^{2}}}(x+y) d y d x\) after changing the order of integration. (a) \(\int_{0}^{2} \int_{0}^{\sqrt{ \left.1-y^{2}\right)}}(x+y) d x d y\) (b) \(\int_{0}^{1} \int_{0}^{\sqrt{1-y^{2} 1}}(x+y) d x d y\) (c) \(\int_{4}^{1} \int_{0}^{\sqrt{\left(1+y^{2}\right)}}(x+y) d x d y\) (d) \(\int_{0}^{-1} \int_{0}^{\sqrt{1-y^{\prime}}}(x+y) d x d y\).
