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....
Find the length of the curve y=coshx with ln2≤x≤ln4. Arc Length: Whenever we need to find the length of a curve, we can always take advantage of one of the many forms of the arc length formula. Here we have quite the typical situation of a curved des...
Find the length of the curve f(x)=x−1 for x∈[1,5]. Length Of The Curve The length of a curve for a function, y=f(x), over a given interval, [a,b], can be found using the formula L=∫ab1+(dydx)2dx where, dydx is the first derivative of the function...
Find the length of the curve x = 4 \cos 5t, y = 20t + 4\sin 5t; \quad 0 \leq t \leq \pi/5 Find the length of the curve y = \int_{1}^{x} \sqrt{t^3-1}\, dt ; \quad 1 \leq x \leq 4 Find the length of the curve y = 2x^(3/2...
Find the length of the curve x=−6cos(θ),y=−6sin(θ),0≤θ≤π. Arc Length: The arc length of a curve is calculated by integrating the arc length differential along the desired interval. The arc length differential for a parametric...
结果一 题目 Use the formula in Exercise to find the torsion of the curve . 答案 , , 相关推荐 1Use the formula in Exercise to find the torsion of the curve .反馈 收藏
Recall the arc length of a polar equationr=f(θ)on the intervala,bis given by the following formula. L=∫ab+(drdθ)22dθ Finddrdθ. drdθ= Additional Materials Reading Find the length of the curve over the given interval. ...
To find the length of the arc OA of the curve given by y=aln(a2a2−x2), where O(0,0) and A(a2,aln43), we will use the formula for the arc length of a curve defined by a function y=f(x): L=∫x2x1√1+(dydx)2dx Step 1: Find dydx First, we need to differentiate y...
Arc length is better defined as the distance along the part of the circumference of any circle or any curve (arc). Any distance along the curved line that makes up the arc is known as the arc length. A part of a curve or a part of a circumference of a circle is called Arc. All ...
(x)=√[(x+4)^2-1], we will now square both sides of the function of the derivative. That is [f'(x)]^2 = [√[(x+4)^2-1]]^2, which gives us [f'(x)]^2 = (x + 4)^2 – 1. We now substitute this expression into the arc length formula/Integral of, s. then ...