Question:medium

If \( \lim_{x \to \frac{\pi}{2}} \dfrac{b(1 - \sin x)(\pi - 2x)^2}{1} = \frac{1}{3} \), then \( \int_0^{3b-6} |x^2 + 2x - 3| \, dx \) is equal to:

Updated On: Apr 9, 2026

3
4
\(\frac{7}{4}\)
2

Show Solution

The Correct Option is B

Solution and Explanation

Was this answer helpful?

0

Top Questions on Calculus

Statement 1: \( f(x) = e^{|\sin x| - |x|} \) is differentiable for all \( x \in \mathbb{R} \).
Statement 2: \( f(x) \) is increasing in \( x \in \left( -\pi, -\frac{\pi}{2} \right) \).
- JEE Main - 2026
- Mathematics
- Calculus
View Solution
The value of \[ \int_0^{2} \sqrt{\frac{x(x^2+x+1)}{(x+1)(x^4+x^2+1)}} \, dx \] is
- JEE Main - 2026
- Mathematics
- Calculus
View Solution
Let \( f(x) = \dfrac{x-1}{x+1} \), \( f^{(1)}(x) = f(x) \), \( f^{(2)}(x) = f(f(x)) \), and \( g(x) + f^{(2)}(x) = 0 \). The area of the region enclosed by the curves \( y = g(x) \), \( y = 0 \), \( x = 4 \), and \( 2y = 2x - 3 \) is:
- JEE Main - 2026
- Mathematics
- Calculus
View Solution
If \(\int_0^{\pi/4} \left[ \cot(x - \frac{\pi}{3}) - \cot(x + \frac{\pi}{3}) + 1 \right] dx = \alpha \log(\sqrt{3} - 1)\) then \(9\alpha\) is
- JEE Main - 2026
- Mathematics
- Calculus
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in JEE Main exam

Potential energy of a particle is given as \( u = \dfrac{A\sqrt{x}}{B+x} \). Find the dimensions of \(A\) and \(B\).

JEE Main - 2026
thermal properties of matter

\( E^0_{\text{Fe}^{2+}/\text{Fe}} \) / Fe = x volts, \( E^0_{\text{Fe}^{3+}/\text{Fe}^{2+}} \) = y volts.
Calculate \( E^0_{\text{Fe}^{2+}/\text{Fe}^{3+}} \) in volts.

JEE Main - 2026
Electrochemistry

If \( \alpha = 3 + 4 + 8 + 9 + 13 + \dots \) up to 40 terms and \( (\tan \beta)^{\frac{\alpha}{1020}} \) is the root of the equation \( x^2 - x - 2 = 0 \), then the value of \( \sin^2 \beta + 3\cos^2 \beta \) is:

JEE Main - 2026
sequences

Let \( \frac{x^2}{f(a^2 + 2a + 7)} + \frac{y^2}{f(3a + 14)} = 1 \) represent an ellipse. The major axis of the given ellipse is the y-axis and \( f \) is a decreasing function. If the range of \( a \) is \( R - [\alpha, \beta] \), then \( \alpha + \beta \) is:

JEE Main - 2026
Straight lines