Let f(x)= _ a ^ x g(t) d t , where g is a non-zero even function. If f(x+5)=g(x) , then _…
Mathematics · JEE Main · NTA Exams — Integral Calculus
Let \(f(x)=\int_{a}^{x} g(t) d t\), where g is a non-zero even function. If \(f(x+5)=g(x)\), then \(\int_{a}^{\infty} f(t) d t\) equals
- \(5 \int_{x+5}^{5} g(t) d t\)
- \(2 \int_{5}^{x+5} g(t) d t\)
- \(\int_{5}^{x+5} g(t) d t\)
- \(\int_{x+5}^{5} g(t) d t\)
Answer
(D) _ x+5 ^ 5 g(t) d t
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