Find the arc length of the curve x = 2 3 ( y − 1 ) 3 / 2 x = \frac{2}{3}(y-1)^{3/2} x = 3 2 ( y − 1 ) 3/2 y = 16 y = 16 y = 16 y = 25 y = 25 y = 25
Find a curve through the point ( 2 , − 4 ) (2, -4) ( 2 , − 4 ) y = 1 y = 1 y = 1 y = 2 y = 2 y = 2 ∫ 1 2 1 + ( 4 y 3 ) 2 d y
\displaystyle \int_{1}^{2} \sqrt{1 + \left( \frac{4}{y^3} \right)^2} \, dy ∫ 1 2 1 + ( y 3 4 ) 2 d y
Find the length of the curve from one point to another using integration and calculus techniques for calculating arc length.
Find the arc length of the parametric curve given by x ( t ) = 2 + 6 t 2 x(t) = 2 + 6t^2 x ( t ) = 2 + 6 t 2 y ( t ) = 5 + 4 t 3 y(t) = 5 + 4t^3 y ( t ) = 5 + 4 t 3 t t t [ 0 , 8 ] [0, \sqrt{8}] [ 0 , 8 ]
Find the arc length of the parametric curve given by x ( t ) = 9 t 2 x(t) = 9t^2 x ( t ) = 9 t 2 y ( t ) = 9 t − 3 t 3 y(t) = 9t - 3t^3 y ( t ) = 9 t − 3 t 3 t t t [ 0 , 2 ] [0, 2] [ 0 , 2 ]
Consider the arc on the curve y = ln ( x 2 − 1 ) y=\ln(x^2-1) y = ln ( x 2 − 1 ) x = 2 x=2 x = 2 x = 8 x=8 x = 8
Given x 3 = y 5 + 2 x^3 = y^5 + 2 x 3 = y 5 + 2 y = 1 y = 1 y = 1 y = 3 y = 3 y = 3
Given a function, find the arc length from x = a x = a x = a x = b x = b x = b ∫ a b 1 + ( f ′ ( x ) ) 2 d x \int_a^b \sqrt{1 + (f'(x))^2} \, dx ∫ a b 1 + ( f ′ ( x ) ) 2 d x
Using integration, find the exact length around the curve from point A to point B for a given function f(x) .
Evaluate the integral from 1 to infinity of ∫ 1 ∞ 1 x d x \displaystyle \int_{1}^{\infty} \frac{1}{x} \, dx ∫ 1 ∞ x 1 d x
Integrate 1 x 2 \frac{1}{x^2} x 2 1
Determine if the integral of ∫ 1 ( 3 x + 1 ) 2 d x \displaystyle \int \frac{1}{(3x + 1)^2} \, dx ∫ ( 3 x + 1 ) 2 1 d x
Evaluate the improper integral ∫ 1 ∞ 1 x 2 d x \displaystyle \int_{1}^{\infty} \frac{1}{x^2} \, dx ∫ 1 ∞ x 2 1 d x
Evaluate lim B → ∞ ∫ 1 B 1 x d x \lim_{{B \to \infty}} \displaystyle \int_{{1}}^{{B}} \frac{1}{x} \, dx lim B → ∞ ∫ 1 B x 1 d x
Evaluate the limit lim B → ∞ ∫ 1 B 1 x n d x \lim_{{B \to \infty}} \int_{{1}}^{{B}} \frac{1}{x^n} \, dx lim B → ∞ ∫ 1 B x n 1 d x n n n
Evaluate the integral ∫ 1 ∞ e − 2 x d x \displaystyle \int_{1}^{\infty} e^{-2x} \, dx ∫ 1 ∞ e − 2 x d x
Evaluate lim B → ∞ ∫ 0 B cos x d x \displaystyle \lim_{{B \to \infty}} \int_{{0}}^{{B}} \cos x \, dx B → ∞ lim ∫ 0 B cos x d x
Evaluate lim a → − ∞ ∫ a 0 e x d x \lim_{{a \to -\infty}} \int_{{a}}^{{0}} e^x \, dx lim a → − ∞ ∫ a 0 e x d x
Evaluate the integral ∫ 0 9 1 x d x
\displaystyle \int_{0}^{9} \frac{1}{\sqrt{x}} \, dx
∫ 0 9 x 1 d x
Evaluate the integral ∫ C 9 x 2 d x \displaystyle \int_{C}^{9} x^2 \, dx ∫ C 9 x 2 d x C → 0 + C \to 0^+ C → 0 +