JEE Mains · Maths · STD 12 - 8. Application and integration
The area (in sq. units) of the region described by \(\left\{(\mathrm{x}, \mathrm{y}): \mathrm{y}^2 \leq 2 \mathrm{x}\right.\), and \(\left.\mathrm{y} \geq 4 \mathrm{x}-1\right\}\) is
- A \(\frac{11}{32}\)
- B \(\frac{8}{9}\)
- C \(\frac{11}{12}\)
- D \(\frac{9}{32}\)
Answer & Solution
Correct Answer
(D) \(\frac{9}{32}\)
Step-by-step Solution
Detailed explanation
\(\text { Shaded area }=\int_{-\frac{1}{2}}^1\left(x_{\text {Right }}-x_{\text {Left }}\right) d y\) \(\begin{aligned} & y^2=2 x \\ & y=4 x-1 \quad \text { Solve } \\ & y=1, y=-\frac{1}{2}\end{aligned}\)…
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