Area Bounded by Miscellaneous Curves and Shapes
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Application of the Integrals

87041 The area of the region bounded by \(y=-1\), \(y=2, x=y^{3}\) and \(x=0\) is

1 \(\frac{17}{4}\) squnits
2 \(\frac{1}{4}\) squnit
3 4 sq units
4 none of these
Manipal-2012
Application of the Integrals

87069 Let \(\mathrm{f}:[-1,2] \rightarrow(0, \infty)\) be a continuous function such that \(\mathbf{f}(\mathbf{x})=\mathbf{f}(\mathbf{1}-\mathbf{x}), \forall \mathbf{x} \in[-\mathbf{1}, \mathbf{2}]\). If \(R_{1}=\int_{-1}^{2} x f(x) d x\) and \(R_{2}\) is the area of the region bounded by \(y=f(x), x=-1, x=2\) and the \(X\) axis. Then

1 \(2 R_{1}=R_{2}\)
2 \(\mathrm{R}_{1}=2 \mathrm{R}_{2}\)
3 \(\mathrm{R}_{1}=3 \mathrm{R}_{2}\)
4 \(3 \mathrm{R}_{1}=\mathrm{R}_{2}\)
MHT CET-2022
NEET DIGITAL LIBRARY
Application of the Integrals

87041 The area of the region bounded by \(y=-1\), \(y=2, x=y^{3}\) and \(x=0\) is

1 \(\frac{17}{4}\) squnits
2 \(\frac{1}{4}\) squnit
3 4 sq units
4 none of these
Manipal-2012
Application of the Integrals

87069 Let \(\mathrm{f}:[-1,2] \rightarrow(0, \infty)\) be a continuous function such that \(\mathbf{f}(\mathbf{x})=\mathbf{f}(\mathbf{1}-\mathbf{x}), \forall \mathbf{x} \in[-\mathbf{1}, \mathbf{2}]\). If \(R_{1}=\int_{-1}^{2} x f(x) d x\) and \(R_{2}\) is the area of the region bounded by \(y=f(x), x=-1, x=2\) and the \(X\) axis. Then

1 \(2 R_{1}=R_{2}\)
2 \(\mathrm{R}_{1}=2 \mathrm{R}_{2}\)
3 \(\mathrm{R}_{1}=3 \mathrm{R}_{2}\)
4 \(3 \mathrm{R}_{1}=\mathrm{R}_{2}\)
MHT CET-2022
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