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Find the area between the x -axis and the graph y = 2 x 3 from x = 1 to x = 5.
54 square units
312 square units
122 square units
212 square units
2x^3
just a simple integral:
∫[1,5] 2x^3 dx = 1/2 x^4 [1,5] = 1/2 (625-1) = 312
To find the area between the x-axis and the graph of y = 2x^3 from x = 1 to x = 5, you can use integration. The area under a curve can be found by evaluating the definite integral of the function from the lower limit to the upper limit.
The definite integral of y = 2x^3 with respect to x, from 1 to 5, can be computed as follows:
∫[1 to 5] 2x^3 dx = [x^4] [1 to 5]
= (5^4) - (1^4)
= 625 - 1
= 624 square units.
Therefore, the area between the x-axis and the graph y = 2x^3 from x = 1 to x = 5 is 624 square units.
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