TS EAMCET · Maths · Definite Integration
If \(f(x)=\int_x^{x+1} e^{-t^2} d t\), then the interval in which \(f(x)\) is decreasing is
- A \(\left(-\frac{1}{2}, \infty\right)\)
- B \((-\infty, 2)\)
- C \((-\infty, 0)\)
- D \((-2,2)\)
Answer & Solution
Correct Answer
(A) \(\left(-\frac{1}{2}, \infty\right)\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} & f(x)=\int_x^{x+1} e^{-t^2} d t \Rightarrow f^{\prime}(x)=e^{-(x+1)^2}-e^{-x^2} \\ & f^{\prime}(x)=\frac{1}{e^{(x+1)^2}}-\frac{1}{e^{x^2}} \end{aligned} \] Since, \(f(x)\) is decreasing function.…
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