What is the area between the graph of y=x^3 and the axis from x=3 to x=4?
2 Answers
Explanation:
We're trying to find
Since
Explanation:
#"the area under a curve is found using"#
#•color(white)(x)"area(A) "=int_a^bydx#
#rArrA=int_3^4x^3dx#
#"integrate using the "color(blue)"power rule"#
#•color(white)(x)int(ax^n)dx=a/(n+1)x^(n+1)to(n!=-1)#
#rArrint_3^4x^3dx=[1/4x^4]_3^4#
#"to evaluate consider"#
#intf(x)dx=F(x)+c#
#rArrint_a^bf(x)=(F(b)+c]-[F(a)+c]=F(b)-F(a)#
#"that is evaluate at x =b and x = a and subtract"#
#rArr[1/4x^4]_3^4#
#=(1/4xx4^4)-(1/4xx3^4)#
#=64-81/4=256/4-81/4=175/4to(B)#