![[Graphics:Images/RiemannSumMod_gr_17.gif]](../Images/RiemannSumMod_gr_17.gif){kind=small}
over ![[Graphics:Images/RiemannSumMod_gr_18.gif]](../Images/RiemannSumMod_gr_18.gif){kind=small}
. Use
the left Riemann sum with n = 25, 50, and
100 to approximate the value of the integral.Example
1. Let over . Use
the left Riemann sum with n = 25, 50, and
100 to approximate the value of the integral.
Solution 1.
![[Graphics:../Images/RiemannSumMod_gr_19.gif]](../Images/RiemannSumMod_gr_19.gif)
![[Graphics:../Images/RiemannSumMod_gr_20.gif]](../Images/RiemannSumMod_gr_20.gif)
![[Graphics:../Images/RiemannSumMod_gr_25.gif]](../Images/RiemannSumMod_gr_25.gif)
![[Graphics:../Images/RiemannSumMod_gr_30.gif]](../Images/RiemannSumMod_gr_30.gif)
(c) John H. Mathews 2004
![[Graphics:../Images/RiemannSumMod_gr_21.gif]](../Images/RiemannSumMod_gr_21.gif){kind=small}
![[Graphics:../Images/RiemannSumMod_gr_22.gif]](../Images/RiemannSumMod_gr_22.gif){kind=small}
![[Graphics:../Images/RiemannSumMod_gr_23.gif]](../Images/RiemannSumMod_gr_23.gif){kind=small}
![[Graphics:../Images/RiemannSumMod_gr_24.gif]](../Images/RiemannSumMod_gr_24.gif)
![[Graphics:../Images/RiemannSumMod_gr_26.gif]](../Images/RiemannSumMod_gr_26.gif){kind=small}
![[Graphics:../Images/RiemannSumMod_gr_27.gif]](../Images/RiemannSumMod_gr_27.gif){kind=small}
![[Graphics:../Images/RiemannSumMod_gr_28.gif]](../Images/RiemannSumMod_gr_28.gif){kind=small}
![[Graphics:../Images/RiemannSumMod_gr_29.gif]](../Images/RiemannSumMod_gr_29.gif)
![[Graphics:../Images/RiemannSumMod_gr_31.gif]](../Images/RiemannSumMod_gr_31.gif){kind=small}
![[Graphics:../Images/RiemannSumMod_gr_32.gif]](../Images/RiemannSumMod_gr_32.gif){kind=small}
![[Graphics:../Images/RiemannSumMod_gr_33.gif]](../Images/RiemannSumMod_gr_33.gif){kind=small}