How to find area of region of the curve y = 4x^3 , the line x = 2 ?

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Answer 1 · 2018-07-22T18:29:45

#16\ \text{unit}^2#

The area of the region bounded by the curve #y=4x^3# & the line #x=2# & the x-axis will be given as

#\int y\ dx#

Applying proper limits for the bounded region, we get required area

#\int_0^2 y\ dx#

#=\int_0^2 4x^3\ dx#

#=4[x^4/4]_0^2#

#=2^4-0#

#=16#

The area of bounded region is #16\ \text{unit}^2#