AP EAMCET · Maths · Definite Integration
If \(\int_0^{10} f(x) d x=5\), then \(\sum_{k=1}^{10} \int_0^1 f(k-1+x) d x=\)
- A 50
- B 10
- C 5
- D 20
Answer & Solution
Correct Answer
(C) 5
Step-by-step Solution
Detailed explanation
Let \(I=\int_0^1 f(k-1+x) d x\) Put \(k-1+x=t \Rightarrow d x=d t\) Limits: \[ \begin{aligned} & x=0 \Rightarrow t=k-1 \\ & x=1 \Rightarrow t=k \end{aligned} \] \[ \therefore \quad I=\int_{k-1}^k f(t) d t \] It can also be written as,…
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