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Find the area under the curve y = x^4 from x = 0 to x = 1.
Find the area under the curve y = x^4 from x = 0 to x = 1.
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Practice Questions
1 question
Q1
Find the area under the curve y = x^4 from x = 0 to x = 1.
1/5
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The area under the curve y = x^4 from 0 to 1 is given by ∫(from 0 to 1) x^4 dx = [x^5/5] from 0 to 1 = 1/5.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the area under the curve y = x^4 from x = 0 to x = 1.
Solution:
The area under the curve y = x^4 from 0 to 1 is given by ∫(from 0 to 1) x^4 dx = [x^5/5] from 0 to 1 = 1/5.
Steps: 8
Show Steps
Step 1: Understand that we want to find the area under the curve of the function y = x^4 between x = 0 and x = 1.
Step 2: To find the area under the curve, we need to calculate the definite integral of the function from 0 to 1.
Step 3: Write the integral as ∫(from 0 to 1) x^4 dx.
Step 4: Find the antiderivative of x^4. The antiderivative is (x^5)/5.
Step 5: Now, we need to evaluate this antiderivative from 0 to 1. This means we will calculate (1^5)/5 - (0^5)/5.
Step 6: Calculate (1^5)/5, which is 1/5, and (0^5)/5, which is 0.
Step 7: Subtract the two results: 1/5 - 0 = 1/5.
Step 8: Therefore, the area under the curve y = x^4 from x = 0 to x = 1 is 1/5.
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