Question:
The value of \(∫(5x-2)^3\) dx is:
The value of \(∫(5x-2)^3\) dx is:
Updated On: May 11, 2025
- 3(5x-2)+C; C is constant of integration.
- 15(5x-2)2+C; C is constant of integration.
- (5x-2)4+C; C is constant of integration.
- \(\frac{(5x-2)^4}{20}\)+C;C is constant of integration.
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
To solve the integral \(∫(5x-2)^3\,dx\), we use the substitution method. Let \(u=5x-2\), then \(du=5\,dx\) or \(dx=\frac{du}{5}\). The integral becomes:
\[∫u^3\cdot\frac{1}{5}\,du\]
Simplifying, we have:
\[\frac{1}{5}∫u^3\,du\]
Integrate \(u^3\):
\[\frac{1}{5}\cdot\frac{u^4}{4}+C=\frac{u^4}{20}+C\]
Substitute back \(u=5x-2\):
\[\frac{(5x-2)^4}{20}+C\]
This matches the correct answer: \(\frac{(5x-2)^4}{20}+C; C\) is the constant of integration.
Was this answer helpful?
0
0
Top Questions on Integration
- Evaluate the integral: \[ \int \frac{\sqrt{\tan x}}{\sin x \cos x} \, dx \]
- MHT CET - 2025
- Mathematics
- Integration
Draw a rough sketch for the curve $y = 2 + |x + 1|$. Using integration, find the area of the region bounded by the curve $y = 2 + |x + 1|$, $x = -4$, $x = 3$, and $y = 0$.
- A woman discovered a scratch along a straight line on a circular table top of radius 8 cm. She divided the table top into 4 equal quadrants and discovered the scratch passing through the origin inclined at an angle \( \frac{\pi}{4} \) anticlockwise along the positive direction of x-axis. Find the area of the region enclosed by the x-axis, the scratch and the circular table top in the first quadrant, using integration.
- If $ \int \left( \frac{1}{x} + \frac{1}{x^3} \right) \left( \sqrt[23]{3x^{-24}} + x^{-26} \right) \, dx $ is equal to $ -\frac{\alpha}{3(\alpha + 1)} \left( 3x^\beta + x^\gamma \right)^{\alpha + 1} + C, \quad x>0, $ where $ \alpha, \beta, \gamma \in \mathbb{Z} $ and $ C $ is the constant of integration, then $ \alpha + \beta + \gamma $ is equal to _______.
- JEE Main - 2025
- Mathematics
- Integration
- Let $ f(x) = \int x^3 \sqrt{3-x^2} dx $. If $ 5f(\sqrt{2}) = -4 $, then $ f(1) $ is equal to
- JEE Main - 2025
- Mathematics
- Integration
View More Questions
Questions Asked in CUET exam
- Pointing to a man, Rani says, "He is the son of my mother's only daughter.” How is the man related to Rani?
- CUET (UG) - 2025
- Blood Relations
- A and B can complete a task in the ratio 3:2. If together they complete the task in 20 days, how long will A alone take?
- CUET (UG) - 2025
- Time and Work
Identify the part of the sentence that contains a grammatical error:
Each of the boys have submitted their assignment on time.- CUET (UG) - 2025
- Subject-Verb Agreement
- If \( 3 \times 4 = 25 \), \( 5 \times 2 = 27 \), \( 6 \times 3 = 39 \), then what is \( 7 \times 5 = ? \)
- CUET (UG) - 2025
- Logical Reasoning
Rearrange the following parts to form a meaningful and grammatically correct sentence:
P. a healthy diet and regular exercise
Q. are important habits
R. that help maintain good physical and mental health
S. especially in today's busy world- CUET (UG) - 2025
- Sentence Arrangement
View More Questions