AP EAMCET · Maths · Definite Integration
If \(\int_{\mathrm{n}}^{\mathrm{n}+1} \mathrm{~g}(\mathrm{x}) \mathrm{dx}=\mathrm{n}^2, \forall \mathrm{n} \in \mathbb{Z}\), then the value of \(\int_{-3}^3 \mathrm{~g}(\mathrm{x}) \mathrm{dx}\) is
- A \(19\)
- B \(28\)
- C \(9\)
- D \(27\)
Answer & Solution
Correct Answer
(A) \(19\)
Step-by-step Solution
Detailed explanation
Given, \(\int_n^{n+1} g(x) d x=n^2, \forall n \in Z\) at \(n=-3, \int_{-3}^{-2} g(x) d x=9\) ...(i) at \(\mathrm{n}=-2, \int_{-2}^{-1} g(x) d x=4\) ...(ii) at \(\mathrm{n}=-1, \int_{-1}^0 g(x) d x=1\) ...(iii) at \(\mathrm{n}=0, \int_0^1 g(x) d x=0\) ...(iv) at…
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