Evaluate the line integral (x+ 1 ds along the curve C given by r (t) = (2 sint, 2 cost), 0

Q: Find the derivative dydx of the parametrically defined function x=t+2sinπt, y=3t−cosπt at t=12

A: Given X=t+ 2 sinπt        and   y = 3t- cosπt We have to find dy/dx at t=12 Method used  Chain…

Q: Compute the area bounded by the cardioid r(0) =1– sin(0) on 0, Express your answer as a decimal…

A:

Q: cr3+lnx etermine the equation of the tangent line to the graph of f(x) = V3+ 5t5 dt at x = 1.

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Q: Use implicit differentiation to find given the relation arctan(5x + y) = 5x2. dx

A: First do some simplification of given relation than use the chain rule of derivative and simplify.

Q: What is the slope of the line tangent to the curve X = (1 + sin t) cost, y = (1 + sin t) sint at t =…

A: x=(1+sin⁡t)cos⁡t,y=(1+sin⁡t)sin⁡t at t=π

Q: a projectile launched at t=0 (t is measured in seconds) follows a path given by x=30t, y=-5t^2+80t,…

A: Given, a projectile launched at t = 0 second that follows a path x=30t, y=-5t^2+80t where x…

Q: A tiny, not scary at all, bug lands on a piece of graph paper and walks along a path so that t…

A: x=4−t3y=5t2+1

Q: Evaluate dy/dx at x = 2 for the function below. y = 8u^2 + 3u – 4, where u =  7x^2 + 3x – 3

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.