AP EAMCET · Maths · Definite Integration
\(\int_{-1}^1\left(\sqrt{1+x+x^2}-\sqrt{1-x+x^2}\right) d x=\)
- A 2
- B 4
- C 0
- D 8
Answer & Solution
Correct Answer
(C) 0
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } \int_{-a}^a f(x) d x=\int_0^a[f(x)+f(-x)] d x \\ & =\int_0^1\left(\sqrt{1+x+x^2}-\sqrt{1-x+x^2}\right) d x \\ & +\int_0^1\left(\sqrt{1-x+x^2}-\sqrt{1+x+x^2}\right) d x=\int_0^1 0 \cdot d x=0 .\end{aligned}\)
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