Express the integral below as the limit of a Riemann Sum. Be sure to specify your choice of ci's, and deltax 5| x^4-7x dx | 0DeltaX= ci= lim ...
Express the integral below as the limit of a Riemann Sum. Be sure to specify your choice of ci's, and deltax
| x^4-7x dx
You should find the area under the given curve, hence, you need to evaluate the limit of sum of areas of n rectangles as the number of rectangles under the curve approaches to infinite.
You need to consider the width of rectangle as `Delta x` and the height of rectangle as `f(x_i) ` .
You need to evaluate in case of n rectangles such that:
`Delta x = (5-0)/n =gtDelta x = 5/n`
You need to evaluate the area of rectangle using the right points such that:
`A = f(x_i)*Delta x`
`x_i = 0+i*Delta x =gtx_i =5i/n`
`f(x_i) = x_i^4 - 7x_i =gt f(x_i) = 625(i/n)^4 - 35i/n`
`A = (625(i/n)^4 - 35i/n)*(5/n)`
`A = 3125i^4/(n^5) - 175i/(n^2)`
Hence, evaluating the area under the curve as the number of rectangles approaches to infinite yields:
`A = lim_(n-gtoo) sum_(i=1)^n(3125i^4/(n^5) - 175i/(n^2))`