AP EAMCET · Maths · Definite Integration
Find the value of ' \(k\) ', if it is given that \(\int_0^{b-c} f(x+c) d x=k \int_c^b f(x) d x\)
- A 1
- B 2
- C 0
- D -2
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
\(I=\int_0^{b-c} f(x+c) d x\) Put \(x+c=t\), then at \(x=0, t=c\) and at \(x=b-c, t=b\) and \(d x=d t\), so \(I=\int_c^b f(t) d t=\int_c^b f(x) d x \Rightarrow \int_0^b f(x+c) d x=\int_c^b f(x) d x\) Therefore \(k=1\)
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