Question
Mathematics Question on Maxima and Minima
Calculate the area under the curve y=2x and included between the lines x=0,x=4.
A
(A) 325
B
(B) 323
C
(C) 312
D
(D) 32
Answer
(B) 323
Explanation
Solution
Explanation:
Given here, y=2x∴y2=4x(x≥0)We need to determine area under curve y2=4x(x≥0) included between the lines x=0,x=4 as:
So, the area under curve will be given as:=∫042xdx=2∫04x12dxWe know that:∫xndx=xn+1n+1xm+n=(xm)(xn)Therefore,2∫04x12dx=2[x1+121+(12)]04=2[x1+(12)32]04=2[23((4)1+(12)−0)]=2[23((4)1(4)12)]=(2)(2)(4)(2)3=323 sq unitsHence, the correct option is (B).