Alerts
Wishlist
Cart
Sign In
Categories
Current Affairs & GK
Current Affairs
Show All Current Affairs & GK
eBooks
General Aptitude
Arithmetic Aptitude
Data Interpretation
Show All General Aptitude
General Knowledge
Basic General Knowledge
General Science
Show All General Knowledge
Medical Science
Anatomy
Biochemical Engineering
Biochemistry
Biotechnology
Microbiology
Show All Medical Science
Technical
Database
Digital Electronics
Electronics
Networking
Show All Technical
Verbal and Reasoning
Logical Reasoning
Verbal Ability
Verbal Reasoning
Show All Verbal and Reasoning
›
Find the value of the integral ∫(0 to 1) (x^2 + 2x)dx.
Find the value of the integral ∫(0 to 1) (x^2 + 2x)dx.
Expand All
Collapse All
Practice Questions
1 question
Q1
Find the value of the integral ∫(0 to 1) (x^2 + 2x)dx.
1
2
3
4
Show Solution
Copy
The integral evaluates to [(1/3)x^3 + x^2] from 0 to 1 = (1/3 + 1) - 0 = 4/3.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the value of the integral ∫(0 to 1) (x^2 + 2x)dx.
Solution:
The integral evaluates to [(1/3)x^3 + x^2] from 0 to 1 = (1/3 + 1) - 0 = 4/3.
Steps: 9
Show Steps
Step 1: Identify the integral you need to solve: ∫(0 to 1) (x^2 + 2x)dx.
Step 2: Break down the integral into two parts: ∫(0 to 1) x^2 dx + ∫(0 to 1) 2x dx.
Step 3: Find the antiderivative of x^2. The antiderivative is (1/3)x^3.
Step 4: Find the antiderivative of 2x. The antiderivative is x^2.
Step 5: Combine the antiderivatives: (1/3)x^3 + x^2.
Step 6: Evaluate the combined antiderivative from 0 to 1: [(1/3)(1)^3 + (1)^2] - [(1/3)(0)^3 + (0)^2].
Step 7: Calculate the value at the upper limit (1): (1/3) + 1 = 4/3.
Step 8: Calculate the value at the lower limit (0): 0.
Step 9: Subtract the lower limit value from the upper limit value: (4/3) - 0 = 4/3.
Related Questions
F
Find the value of tan(45°).
Question: Find the value of tan(45°).Options: 01undefined√3Correct Answer: 1Solution: tan(45°) = 1...
W
What is the derivative of f(x) = x^3 - 3x^2 + 4x - 5?
Question: What is the derivative of f(x) = x^3 - 3x^2 + 4x - 5?Options: 3x^2 - 6x + 43x^2 - 6x2x^2 -..
W
What is the value of 5C2?
Question: What is the value of 5C2?Options: 1020155Correct Answer: 10Solution: 5C2 = 5! / (2!(5-2)!)..
W
What is the value of the limit lim (x -> 0) (sin(5x)/x)?
Question: What is the value of the limit lim (x -> 0) (sin(5x)/x)?Options: 01510Correct Answer: 5Sol..
I
If the coordinates of points A and B are (1, 2) and (3, 4) respectively, what is
Question: If the coordinates of points A and B are (1, 2) and (3, 4) respectively, what is the dista..
‹
Biology (School & UG)
Chemistry (School & UG)
Civil Engineering
Commerce & Accountancy
Computer Science & IT
Current Affairs & GK
Data Structures & Algorithms
eBooks
Electrical & Electronics Engineering
English (School)
General Aptitude
General Knowledge
General Knowledge & Current Affairs
Languages & Literature
Law & Legal Studies
Major Competitive Exams
Mathematics (School)
Mechanical Engineering
Medical Science
Physics (School & Undergraduate)
Quantitative Aptitude & Reasoning
Social Science (School)
Technical
Verbal and Reasoning
Vocational & Skill Development
›
Soulshift Feedback
×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy
?
0
1
2
3
4
5
6
7
8
9
10
Not likely
Very likely
✕
↑
