Question:
\(\int \frac{dx}{e^{-x}} \)
\(\int \frac{dx}{e^{-x}} \)
Show Hint
When integrating exponentials of the form \( e^x \), the result is simply \( e^x + k \).
Updated On: Sep 13, 2025
- \( - \frac{1}{e^{-x}} + k \)
- \( e^x + k \)
- \( \frac{1}{e^{-x}} + k \)
- \( -e^{-x} + k \)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
We need to evaluate:
\[
I = \int \frac{dx}{e^{-x}}
\]
This simplifies to:
\[
I = \int e^{x} dx
\]
The integral of \( e^x \) is \( e^x \), so the solution is:
\[
I = e^x + k
\]
Was this answer helpful?
0
0
Top Bihar Board XII Mathematics Questions
- \(\frac{d}{dx} \left(\sec^2 x - \tan^2 x\right)\)
- \(\frac{d}{dx} \left( e^{2x} + 2e^x \right)\)
- \(\frac{d}{dx} \left[ \lim_{x \to a} \frac{x^n + a^n}{x + a} \right] \)
- \(\frac{d}{dx} \left( \sin^{-1} 2x \right)\)
- \(\frac{d}{dx} \left[ (x+2)(x^2 - 2x + 4) \right] \)
View More Questions
Top Bihar Board XII Integration Questions
- \(\int \frac{dx}{x^2 + 4} \)
- \(\int \tan \left( \tan^{-1} x \right) \, dx = ? \)
- \(\int \log x^2 \, dx \)
- \(\int (\sin 3x + 4 \sin^3 x) \, dx \)
- \(\int_{-1}^{1} \sin^7 x \cos^{13} x \, dx = ? \)
View More Questions
Top Bihar Board XII Questions
- Which metal was first used by humans?
- Where is the Harappan site called Shortughai located?
- Where has the evidence of dockyard been found from Indus Valley Civilization?
- Which is referred to as Meluhha in Mesopotamian texts?
- Where have miniature pots of faience probably used as perfume bottles been found?
View More Questions