TS EAMCET · Maths · Definite Integration
A minimum value of \(\int_0^x t e^{t^2} d t\) is
- A 0
- B 1
- C 2
- D 3
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
We have, \(\int_0^x t e^{t^2} d t\) Let \(\quad t^2=z \Rightarrow 2 t d t=d z\) \(f(x)=\int_0^{x^2} \frac{e^z}{2} d z=\frac{1}{2}\left[e^z\right]_0^{x^2}\) \(\Rightarrow \quad f(x)=\frac{1}{2}\left[e^{x^2}-1\right]\) On differentiating both sides w.r.t. \(x\),…
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