How do you find the Riemann sum for #f(x) = 4 sin x#, #0 ≤ x ≤ 3pi/2#, with six terms, taking the sample points to be right endpoints?

1 Answer
Sasha P.
Sep 27, 2015

#(pisqrt2)/2#

Explanation:

#n=6, a=0, b=(3pi)/2#

#Deltax=(b-a)/n=((3pi)/2)/6=(3pi)/12=pi/4#

#S=sum_(i=1)^6 f(x_i)Deltax#

#S=Deltax(f(x_1)+f(x_2)+f(x_3)+f(x_4)+f(x_5)+f(x_6))#

#x_i=a+i*Deltax=0+i*Deltax=i*Deltax#

#f(x_1)=f(pi/4)=4sin(pi/4)=4 sqrt2/2=2sqrt2#
#f(x_2)=f(2pi/4)=4sin(pi/2)=4#
#f(x_3)=f(3pi/4)=4sin(3pi/4)=4 sqrt2/2=2sqrt2#
#f(x_4)=f(4pi/4)=4sin(pi)=0#
#f(x_5)=f(5pi/4)=4sin(5pi/4)=4 (-sqrt2/2)=-2sqrt2#
#f(x_6)=f(6pi/4)=4sin(3pi/2)=4 (-1)=-4#

#S=pi/4(2sqrt2+4+2sqrt2+0-2sqrt2-4)=pi/4 2sqrt2=(pisqrt2)/2#

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