Question:
The value of \(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} (x^2 \sin x + x^3) \, dx\) is:
The value of \(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} (x^2 \sin x + x^3) \, dx\) is:
Updated On: Jul 12, 2024
- \(\frac{1}{2} + \frac{\pi^4}{64}\)
- \(\frac{1}{2} - \frac{\pi^4}{64}\)
- \(0\)
- \(\frac{\pi^4}{64}\)
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The correct option is (C): \(0\)
Was this answer helpful?
0
0
Top Questions on Calculus
- Let \(E_1: \frac{x^2}{9} + \frac{y^2}{4} = 1\) be an ellipse. Ellipses \(E_i\) are constructed such that their centers and eccentricities are the same as that of \(E_1\), and the length of the minor axis of \(E_{i+1}\) is the length of the major axis of \(E_i\). If \(A_i\) is the area of the ellipse \(E_i\), then \(\frac{5}{\pi} \sum_{i=1}^{\infty} A_i\) is equal to:
- The area of the region bounded by the curves \( x(1 + y^2) = 1 \) and \( y^2 = 2x \) is:
- The area (in sq. units) of the region \((x, y) : 0 \leq y \leq 2|x| + 1, 0 \leq y \leq x^2 + 1, |x| \leq 3\) is:
- If \( f(x) = \frac{2^x}{2^x + \sqrt{2}} \), \(x \in \mathbb{R}\), then \(\sum_{k=1}^{81} f\left(\frac{k}{82}\right)\) is equal to:
- Let \( f(x) \) be defined as follows:
\[ f(x) = \begin{cases} 3x, & \text{if } x < 0 \\ \min(1+x+\lfloor x \rfloor, 2+x\lfloor x \rfloor), & \text{if } 0 \leq x \leq 2 \\ 5, & \text{if } x > 2 \end{cases} \]
where \(\lfloor . \rfloor\) denotes the greatest integer function. If \(\alpha\) and \(\beta\) are the number of points, where \(f\) is not continuous and is not differentiable, respectively, then \(\alpha + \beta\) equals:
View More Questions
Questions Asked in NATA exam
- A boy gave a bundle of RS.100 notes to a guy. The serial number of notes are from CJJ103440 to CJJ103490. What is the total amount given to the guy
- NATA - 2024
- General Aptitude
- Mirror image of a clock shows 8:50. What will the actual time?
- NATA - 2024
- General Aptitude
- Find the next number in the series 5, 20, 24, 6, 2, 8,
- NATA - 2024
- General Aptitude
- What is another word for 'LOFT'?
- NATA - 2024
- Architectural Knowledge
- Identify the building material:
- NATA - 2024
- Architectural Knowledge
View More Questions