Problem 1
Find the average value of the function on the given interval. $$ f(x)=4 x^{3} ; \quad[1,3] $$
Problem 1
use the Second Fundamental Theorem of Calculus to evaluate each definite integral. $$ \int_{0}^{2} x^{3} d x $$
Problem 1
Find the value of the indicated sum. $$ \sum_{k=1}^{6}(k-1) $$
Problem 1
Use the methods of (1) left Riemann sum, (2) right Riemann sum, (3) Trapezoidal Rule, (4) Parabolic Rule with \(n=8\) to approximate the definite integral. Then use the Second Fundamental Theorem of Calculus to find the exact value of each integral. $$ \int_{1}^{3} \frac{1}{x^{2}} d x $$
Problem 2
use the Second Fundamental Theorem of Calculus to evaluate each definite integral. $$ \int_{-1}^{2} x^{4} d x $$
Problem 2
Find the average value of the function on the given interval. $$ f(x)=5 x^{2} ; \quad[1,4] $$
Problem 2
Find the value of the indicated sum. $$ \sum_{i=1}^{6} i^{2} $$
Problem 2
Use the methods of (1) left Riemann sum, (2) right Riemann sum, (3) Trapezoidal Rule, (4) Parabolic Rule with \(n=8\) to approximate the definite integral. Then use the Second Fundamental Theorem of Calculus to find the exact value of each integral. $$ \int_{1}^{3} \frac{1}{x^{3}} d x $$
Problem 3
Use the methods of (1) left Riemann sum, (2) right Riemann sum, (3) Trapezoidal Rule, (4) Parabolic Rule with \(n=8\) to approximate the definite integral. Then use the Second Fundamental Theorem of Calculus to find the exact value of each integral. $$ \int_{0}^{2} \sqrt{x} d x $$
Problem 3
Find the average value of the function on the given interval. $$ f(x)=\frac{x}{\sqrt{x^{2}+16}} ; \quad[0,3] $$
