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Question
Fill in the blank :
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _______.
Solution
Let A be the required area.
Consider the equation y = x4.
∴ A = `int_1^5 y*dx`
= `int_1^5 x^4*dx`
= `[(x^5)/5]_1^5`
= `(1)/(5)[x^5]_1^5`
= `(1)/(5)[(5)^5 - (1)^5]`
= `(1)/(5)(3125 - 1)`
∴ A = `(3124)/(5)"sq . units"`.
Notes
Let A be the required area.
Consider the equation y = x4.
∴ A = `int_1^5 y*dx`
= `int_1^5 x^4*dx`
= `[(x^5)/5]_1^5`
= `(1)/(5)[x^5]_1^5`
= `(1)/(5)[(5)^5 - (1)^5]`
= `(1)/(5)(3125 - 1)`
∴ A = `(3124)/(5)"sq . units"`.
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