VIPSolutionsProvide answer without latex723M N RB 79%a {) 25 app.outlierai/screening?id=68a5cc2 + H J)’ Outlier — & 5m maining Evaluate the definite integral [* (Sx” - dv +2) dx © ® 0 & 1 1 vr rt 1 11 1 “111 vr 1 L111 “1 1 111111 238 1 1 1 1 1 1 EEG 1#1 , English(India) . J 9 [1 O Vv
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Provide answer without latex
723M N RB 79%a
{) 25 app.outlierai/screening?id=68a5cc2 + H
J)’ Outlier — & 5m maining
Evaluate the definite integral [* (Sx” - dv +2) dx
© ® 0 &
1 1 vr rt 1 11 1
“111 vr 1 L111
“1 1 111111
238 1 1 1 1 1 1 EEG
1#1 , English(India) . J
9 [1 O Vv
This is AI generated Response.
Asked by: Gurubindra Singh
Created at: 2025-08-20 19:23:45
Asked by: Gurubindra Singh
Created at: 2025-08-20 19:23:45
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Let's solve the definite integral from 1 to 2 of (5x^2 - 4x + 2) dx.
Step 1: Find the indefinite integral.
The integral of 5x^2 is (5/3)x^3.
The integral of -4x is -2x^2.
The integral of 2 is 2x.
So, the indefinite integral is:
(5/3)x^3 - 2x^2 + 2x
Step 2: Evaluate from 1 to 2.
Plug in x = 2:
(5/3)(2^3) - 2(2^2) + 2(2) = (5/3)(8) - 2(4) + 4 = 40/3 - 8 + 4 = 40/3 - 4
Now plug in x = 1:
(5/3)(1^3) - 2(1^2) + 2(1) = 5/3 - 2 + 2 = 5/3
Step 3: Subtract the two results:
[40/3 - 4] - [5/3] = (40/3 - 5/3) - 4 = (35/3) - 4
Step 4: Convert 4 to thirds:
4 = 12/3, so
(35/3) - (12/3) = 23/3
**Final Answer:**
The value of the integral is 23/3.
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