JEE Mains · Maths · STD 12 - 7.1 indefinite integral
Let \(f(x)=\int \frac{d x}{x^{\left(\frac{2}{3}\right)}+2 x^{\left(\frac{1}{2}\right)}}\) be such that \(f(0)=-26+24 \log _{ e }(2)\). If \(f (1)= a + b \log _{ e }(3)\), where \(a , b \in Z\), then \(a + b\) is equal to:
- A \(-18\)
- B \(-5\)
- C \(-11\)
- D \(-26\)
Answer & Solution
Correct Answer
(C) \(-11\)
Step-by-step Solution
Detailed explanation
\(f(x)=\int \frac{d x}{x^{2 / 3}+2 x^{1 / 2}}\) Put \(x=t^6 \Rightarrow d x=6 t^5 d t\) \(=\int \frac{6 t^5 d t}{t^4+2 t^3}=6 \int \frac{\left(t^2-4\right)+4}{t+2} d t\) \(=6\left[\int( t -2) dt +4 \int \frac{1}{ t +2} dt \right]\)…
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