JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \(f(x)\) and \(g(x)\) be two functions satisfying \(f\left(x^{2}\right)\) \(+g(4-x)=4 x^{3}\) and \(g(4-x)+g(x)=0\), then the value of \(\int_{-4}^{4} f(x)^{2} d x\) is
- A \(373\)
- B \(496\)
- C \(584\)
- D \(512\)
Answer & Solution
Correct Answer
(D) \(512\)
Step-by-step Solution
Detailed explanation
\(I =2 \int_{0}^{4} f\left( x ^{2}\right) dx \{\) Even funtion \(\}\) \(=2 \int_{0}^{4}\left(4 x ^{3}- g (4- x )\right) d x\) \(=2\left(\left.\frac{4 x ^{4}}{4}\right|_{0} ^{4}-\int_{0}^{4} g (4- x ) d x \right)\) \(=2(256-0)=512\)
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