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GUJCET · Maths · Integrals
\(\int_0^1(0.001)^{\frac{x}{3}} e^x d x=\) _________.
- A \(\frac{e-10}{10\left(1+\log _{10} e\right)}\)
- B \(\frac{10-10 e}{\left(1+\log _e 10\right)}\)
- C \(\frac{e-10}{10\left(1-\log _e 10\right)}\)
- D \(\frac{10-e}{e\left(1-\log _e 10\right)}\)
Answer & Solution
Correct Answer
(C) \(\frac{e-10}{10\left(1-\log _e 10\right)}\)
Step-by-step Solution
Detailed explanation
\( \int_0^1(0.001)^{\frac{x}{3}} e^x d x = \int_0^1 (10^{-3})^{\frac{x}{3}} e^x d x \) \( = \int_0^1 10^{-x} e^x d x = \int_0^1 e^{-x \ln 10} e^x d x \)
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