Question:
\(\int_0^a e^x \, dx \)
\(\int_0^a e^x \, dx \)
Show Hint
The integral of \( e^x \) is just \( e^x \), and always subtract the limits when solving definite integrals.
Updated On: Sep 13, 2025
- \( e \)
- \( 1 - e \)
- \( e^a - 1 \)
- \( 0 \)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
We are given:
\[
I = \int_0^a e^x \, dx
\]
The integral of \( e^x \) is simply \( e^x \), so:
\[
I = \left[ e^x \right]_0^a = e^a - e^0 = e^a - 1
\]
Thus, the correct answer is \( e^a - 1 \).
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
- \(\int \frac{dx}{x^2 + 4} \)
- \(\int \tan \left( \tan^{-1} x \right) \, dx = ? \)
- \(\int \frac{dx}{e^{-x}} \)
- \(\int \log x^2 \, dx \)
- \(\int (\sin 3x + 4 \sin^3 x) \, dx \)
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