JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \((a, b)\) be the point of intersection of the curve \(x^2=2 y\) and the straight line \(y-2 x-6=0\) in the second quadrant. Then the integral \(I=\int_a^b \frac{9 x^2}{1+5^x} d x\) is equal to :
- A \(24\)
- B \(27\)
- C \(18\)
- D \(21\)
Answer & Solution
Correct Answer
(A) \(24\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & x^2=2 y\ \&\ y=2 x+6 \\ & x^2=4 x+12\end{aligned}\) \(\left.x^2-4 x-12=0 \Rightarrow \begin{gathered}x=6 \\ y=18\end{gathered} \right\rvert\, \begin{gathered}\text { if } x=-2 \\ y=2\end{gathered}\) \(\therefore(6,18)\ \&\ (-2,2)\) Here \((6,18)\) Rejected…
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