MHT CET · Maths · Area Under Curves
Area bounded by the lines \(y=x, x=-1, x=2\) and the \(X\)-axis is
- A \(\frac{1}{2}\) sq. units
- B \(\frac{3}{2}\) sq. units
- C \(\frac{5}{2}\) sq. units
- D \(\frac{7}{4}\) sq. units
Answer & Solution
Correct Answer
(C) \(\frac{5}{2}\) sq. units
Step-by-step Solution
Detailed explanation
Required area shaded
\(\begin{aligned} & A=\int_{-1}^0 x d x+\int_0^2 x d x \\ & =\left|\left[\frac{x^2}{2}\right]_{-1}^0\right|+\left|\left[\frac{x^2}{2}\right]_0^2\right|=\frac{1}{2}+2=\frac{5}{2}\end{aligned}\)
\(\begin{aligned} & A=\int_{-1}^0 x d x+\int_0^2 x d x \\ & =\left|\left[\frac{x^2}{2}\right]_{-1}^0\right|+\left|\left[\frac{x^2}{2}\right]_0^2\right|=\frac{1}{2}+2=\frac{5}{2}\end{aligned}\)
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