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Calculate the area under the curve y = x^4 from x = 0 to x = 2.
Calculate the area under the curve y = x^4 from x = 0 to x = 2.
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Practice Questions
1 question
Q1
Calculate the area under the curve y = x^4 from x = 0 to x = 2.
4
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32
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The area under the curve y = x^4 from x = 0 to x = 2 is given by ∫(from 0 to 2) x^4 dx = [x^5/5] from 0 to 2 = (32/5) - 0 = 32/5.
Questions & Step-by-step Solutions
1 item
Q
Q: Calculate the area under the curve y = x^4 from x = 0 to x = 2.
Solution:
The area under the curve y = x^4 from x = 0 to x = 2 is given by ∫(from 0 to 2) x^4 dx = [x^5/5] from 0 to 2 = (32/5) - 0 = 32/5.
Steps: 8
Show Steps
Step 1: Identify the function you want to find the area under. In this case, the function is y = x^4.
Step 2: Set up the integral to calculate the area under the curve from x = 0 to x = 2. This is written as ∫(from 0 to 2) x^4 dx.
Step 3: Find the antiderivative of the function x^4. The antiderivative is x^5 / 5.
Step 4: Evaluate the antiderivative at the upper limit (x = 2) and the lower limit (x = 0).
Step 5: Calculate the value at the upper limit: (2^5) / 5 = 32 / 5.
Step 6: Calculate the value at the lower limit: (0^5) / 5 = 0.
Step 7: Subtract the lower limit value from the upper limit value: (32/5) - 0 = 32/5.
Step 8: The final result is the area under the curve from x = 0 to x = 2, which is 32/5.
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