How do you Find the Riemann sum for #f(x)=x^3# on the interval #[0,5]# using right endpoints with #n=8#?
By signing up, you agree to our Terms of Service and Privacy Policy
To find the Riemann sum for ( f(x) = x^3 ) on the interval ([0,5]) using right endpoints with ( n = 8 ), follow these steps:

Determine the width of each subinterval: ( \Delta x = \frac{b  a}{n} ), where ( a = 0 ) (the lower limit of the interval), ( b = 5 ) (the upper limit of the interval), and ( n = 8 ).
( \Delta x = \frac{5  0}{8} = \frac{5}{8} )

Determine the right endpoints of each subinterval: ( x_i = a + i \cdot \Delta x ), where ( i = 1, 2, \ldots, n ).
( x_i = 0 + i \cdot \frac{5}{8} ) for ( i = 1, 2, \ldots, 8 ).

Evaluate the function ( f(x) = x^3 ) at each right endpoint.

Multiply each function value by the width of the corresponding subinterval.

Sum up all the products obtained in step 4.
Here's the calculation:

For ( i = 1 ): ( x_1 = \frac{5}{8} ) ( f(x_1) = \left(\frac{5}{8}\right)^3 = \frac{125}{512} )

For ( i = 2 ): ( x_2 = \frac{5}{8} \times 2 = \frac{5}{4} ) ( f(x_2) = \left(\frac{5}{4}\right)^3 = \frac{125}{64} )
Continue this process until ( i = 8 ).
Then, calculate the Riemann sum:
[ R = \frac{5}{8} \left( \frac{125}{512} + \frac{125}{64} + \ldots + \text{all other terms} \right) ]
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 How do you find the area using the trapezoidal approximation method, given #(x²6x+9) dx#, on the interval [0,3] with n=3?
 How do you use the Trapezoidal Rule with n=60 to estimate the length of the curve #y=sinx#, with x greater or equal to 0 and x less than or equal to pi?
 How do you find the area using the trapezoid approximation method, given #sin (x^2) dx#, on the interval [0, 1/2] using n=4?
 Estimate the area under the curve #f(x) = x^2# over the interval #[0,10]# with #5# strips using Left Riemann Sums?
 How do you use the trapezoidal rule with n=6 to approximate the area between the curve #f(x)=x^29# from 3 to 3?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7