The length of the curve determined by the equation y=√ x from x=0 to x=3 is ( ) A. ∫ _0^3√ ( 1(4x)+1)dx B. 2∫ _0^3√ ( 1(2x)+1)dx C. ∫ _0^3√ (x+1)\ dx D. ∫ _0^3√ x\ dx E. ∫ _0^3√ ( 1(4x^2)+1)dx...
Let C be the curve of intersection. The projection of C onto the xy-plane is the ellipse 4x^2+y^2=4 or x^2+(y^2)4=1, z=0. Then we can write x=cos t, y=2sin t, 0≤q t≤q 2π . Since C also lies on the plane x+y+z=2, we have z=2-x-y=2-cos t-2sin t....
Given Equation of the curve y=x2−lnx8 We have length of the curve is {eq}\displaystyle \int_{x=a}^{x=b}...Become a member and unlock all Study Answers Start today. Try it now Create an account Ask a question Our experts can answer your tough hom...
First, find the integral set up, using the arc length formula, then second, find the integral limits and the first-order differentiation of the curve functions. Finally integrate to get the arc length. Answer and Explanation: We have the curve equati...
In the method, the length of the curved crack is taken as the coordinate in the singular integral equation of curve crack problem. The crack configuration maps onto the real axis with interval (,), where 2 is the curve length of the crack. The original singular integral equation is ...
To find the equation of the curve y=f(x) given that the length of the tangent intercepted between the point and the x-axis is of length 1, we can follow these steps: Step 1: Understand the Length of the TangentThe length of the tangent line at a point (x,y) on the curve can ...
Next we'll meet the equation for the length. General Form of the Length of a Curve in Polar Form In general, the arc length of a curver(θ) in polar coordinates is given by: `L=int_a^bsqrt(r^2+((dr)/(d theta))^2)d theta` ...
the curve length is the integration of the curve parametric equation’s derivation. So the core algorithm for curve length calculation is the numerical integration method. OpenCASCADE use Gauss-Legendre to calculate the integration for single variable and multiple variables. Because of curve in OpenCASC...
Find the arc length of the curves {eq}\mathbf r(t) = \langle t^2,t^3\rangle ; \quad 0 \leq t \leq \frac{\sqrt 5}{3} {/eq} Arc Length: To find the arc length if the equation is given in parametric form then we will use the following formula {...
The formula for the arc length is {eq}{\rm{Length}} = \int\limits_a^b {\sqrt {1 + {{\left( {\dfrac{{dy}}{{dx}}} \right)}^2}} dx} {/eq}. Answer and Explanation: Given An equation of curve {eq}y = \dfrac{3}...