Question

Find the area between the curve of y = 3x^6 and the x-axis interval from x = -1 to x = 1.
a. 6/7 units^2
b. 7/6 units^2
c. 9/7 units^2
d. 7/9 units^2

Answer 1

Answer: Letter B

Explanation: Hope It Helps

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Answer 2

The area between the curve and x-axis is 6/7 units²

How can one find out the area between a curve and x-axis using integrals?

By performing a definite integral between the two locations, one can determine the area under a curve between two points. Integrate y = f(x) between the limits of a and b to determine the area under the curve y = f(x) between x = a and x = b. Areas below the x-axis will have a negative result, while those above the x-axis will have a positive result.

Solution:

Given,

curve y= 3x⁶

x-axis interval = ₋1 to 1

area between the curve and the x-axis is limits(-1 to 1) ∫3x⁶

limits(-1 to 1) 3∫x⁶

limits(-1 to 1) 3∫x⁷/7

3[2/7]

6/7 units²

Hence we get the answer as 6/7 units².

Learn more about "Definite Integrals" here-

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