Find the length of the curve.r(t)=<2t,t^2, 13t^3>, 0≤ t≤ 1 相关知识点: 试题来源: 解析 73. r(t)=<2t,t^2, 13t^3> ⇒ \ r'(t)=<2,2t,t^2> ⇒|r'(t)|=√ (2^2+(2t)^2+(t^2)^2)=√ (4+4t^2+t^4)=√ ((2+t^2)^2)=2+t^2 for 0≤ t≤ 1....
百度试题 结果1 题目3. The formula for the length L of the curve x = f(t), 相关知识点: 试题来源: 解析 3. ∫_a^b√(ff^+(t))^2+lg^2(t)]^2dt 反馈 收藏
Find the length of the curve x = 1 + 21t^2, y = 8 + 14t^3, 0 lessthanorequalto t lessthanorequalto 4. . Find the length of the curve y = 4x^\frac{3}{2} from x = 0 to x = \frac{5}{16}. Find the length of the curve y = ln(x) from...
For any function that is continuous, we have to apply the length formula that will be {eq}L=\int_{a}^{b}\sqrt{1+y'^2}dx\\ {/eq} were the function whose arc length is to be evaluated is {eq}y= f(x). {/eq} Now, the arc length...
What is the length of the curve y=ln(sec(x)) from x=0 to x=1? The Arc Length: The arc length of the curve y=f(x) on the closed interval [a , b] is: ∫ab1+(y′)2 dx. To solve this problem, we'll use the above formula.To solve the definite integ...
LengthPerimeterPedal curvePedal pointInterior of a curveSupport functionWinding numberOvalPotential functionIn this article we present a new formula for the length of a closed curve involving a double integral of a certain potential function. This formula is based on the construction of pedal curves,...
To use the arc length formula first we find the derivative by using the chain rule. Next, we try to remove the square root in the size of the tangent vector by completing some squares. Answer and Explanation: Remember that the length of a curve {eq}\displaystyle \, y...
Find the length of the curve forr=1+cos2θ,π/2≤θ≤π/2 Homework Equations integral of [tex]\sqrt{(r^2+(dr/d\theta)^2}[\tex] The Attempt at a Solution i simplified my r to be2∗cosθ after simplification and plugging into the formula. i got my answer to be2∗π...
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 ...
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