AP EAMCET · Maths · Indefinite Integration
If \(f(x)=\int \frac{5 x^8+7 x^6}{\left(x^2+2 x^7+1\right)^2} d x(x \geq 0)\) and \(f(0)=0\), then the value of \(f(1)=\)
- A \(\frac{-1}{2}\)
- B \(\frac{-1}{4}\)
- C \(\frac{1}{4}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {Given } f(x)=\int \frac{5 x^8+7 x^6}{\left(x^2+2 x^7+1\right)^2} d x \\ & \Rightarrow f(x)=\int \frac{5 x^{-6}+7 x^{-8}}{\left(\frac{1}{x^7}+\frac{1}{x^5}+2\right)^2}=\frac{1}{2+\frac{1}{x^7}+\frac{1}{x^5}}+c \end{aligned}\) Since,…
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