JEE Mains · Maths · STD 12 - 7.2 definite integral
For \(m, n > 0\), let \(\alpha(m, n)=\int_0^2 t^m(1+3 t)^n d t\). If \(11 \alpha(10,6)+18 \alpha(11,5)= p (14)^6\), then \(p\) is equal to \(......\).
- A \(31\)
- B \(32\)
- C \(30\)
- D \(33\)
Answer & Solution
Correct Answer
(B) \(32\)
Step-by-step Solution
Detailed explanation
\(\alpha( m , n )=\int \limits_0^2 t ^{ m }(1+3 t )^{ n } dt\) \(\text { If } 11 \alpha(10,6)+18 \alpha(11,5)= p (14)^6 \text { then } P\) \(=11 \int \limits_0^2 \frac{ t ^{10}}{ II } \frac{(1+3 t )^6}{ I }+10 \int^2 t ^{11}(1+3 t )^5 dt\)…
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