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

Q: If the tangent line to y = f(x) at (5, 2) passes through the point (0, 1), find f(5) and f'(5). f(5)…

A:

Q: 2. Find the length of the curve 0<t< 2n. r(t) e'i + e' sin 2tj + e' cos 2tk,

A: From the given problem :   rt=eti+etsin2tj+etcos2tk   So,   x=et, y=etsin2t , z=etcos2t .   As we…

Q: S ize Find an equation of the line tangent to the curve defined by x + 5xy + y² = 7 at the point (1,…

A:

Q: L. Let h (x) = f (x) g (x). Find a. h' (1), b. h' (3), and с. h' (4).

A: According to the given information,

Q: 3. Integrate numerically the given function, f(5+ 3sinx) dx using (a) single application of the…

A:

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

A:

Q: 2x f(x) sec(t*) dt. %3D -2x

A: Given,            f(x) =∫-2x2xsect4 dt

Q: Find f’

A:

Q: Show that both R and R2 may be covered by countably many open balls.

A:

Q: 6. Find the arclength of the curve y Note: L = 1+ (f'(x))² dx √ 1 x²+1 for -2 ≤ x ≤ 2.

A:

Q: (f) y’+sinxy² 3/2

A: Given function

Q: cosh x dy + (y sinh x + ex) dx = 0

A: Step 1:

Q: Ben can wash a car in 2 hours while his younger brother James can do it in 3 hours. How long will it…

A: In 1 hour Ben can wash 12 part of car. in 1 hour his younger brother can wash 13 part of car.

Q: Estimate f(5.03) for f as in the figure. y=f(x) (10, 4) Tangent line (4, 2) (Give your answer to…

A:

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.