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Evaluate ∫ (5 - 3x) dx. (2022)
Evaluate ∫ (5 - 3x) dx. (2022)
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Practice Questions
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Q1
Evaluate ∫ (5 - 3x) dx. (2022)
5x - (3/2)x^2 + C
5x - (3/3)x^2 + C
5x - (3/4)x^2 + C
5x - (3/5)x^2 + C
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The integral is 5x - (3/2)x^2 + C.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate ∫ (5 - 3x) dx. (2022)
Solution:
The integral is 5x - (3/2)x^2 + C.
Steps: 6
Show Steps
Step 1: Identify the function to integrate, which is (5 - 3x).
Step 2: Break down the integral into two parts: ∫5 dx and ∫(-3x) dx.
Step 3: Integrate the first part, ∫5 dx, which gives 5x.
Step 4: Integrate the second part, ∫(-3x) dx. The integral of x is (1/2)x^2, so this part becomes -3 * (1/2)x^2 = -(3/2)x^2.
Step 5: Combine the results from Step 3 and Step 4: 5x - (3/2)x^2.
Step 6: Add the constant of integration, C, to the final result.
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