2. Consider the equation r = sin(n@) for n even and positive. Show that the area is the same regardless of n. n = 2 n = 4 n = 6

Q: Q3/By using matab find the area under the curve f(z) = z cos(z) for -4 SZ<9.

A: The area under any curve f(x) bounded within the interval [a,b] is given by: Area=∫abf(x) dx

Q: Find the area bounded by y = sin?(x) and y = sin³ (x) from -<x<n.

A:

Q: Determine the approximate area under the integral Jo 1ii dx using Trapezoidal with 3 level Rombergs.…

A: Value of definite integral of function represents the amount of area inside the function curve. The…

Q: Find the area that is inside both r=1−sinθ and r=2+sinθ

A: Graph:

Q: 5 Find the area under the curve y over the interval [0, 1]. (4x + 4)2 Enter the exact answer. area =

A:

Q: 4 Find the area bounded by Y 0, y = 0, x = 2. %3D /144 – 16x? Round to four decimal places.

A: We have to use definite integration.

Q: 1. Sketch and find the area defined by y = sinh x, y = e-ª, x =0, x = 2

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: 5. Find the area under the curve 2 dr - x2 9 – where 4 < r< 10

A: To find the area under the curve given by the integrand ∫29-x2dx where 4≤x≤10

Q: 9. Find the area under the curve y (x + 2)? over the interval [ – 1, 1]. area

A:

Q: between

A:

Q: Find the area: y = et and y = 1 and to the right of (e"+1) x.

A: we have to find the area between the curves y=exex+1 and y=1 and to the right of x.

Q: Evaluate the integral and interpret it as the area of a region. я/2 |8 sin(x) – 8 cos(2x)| dx

A: Here this is a tricky question Find where the function is positive and where the function is…

Q: Find the value of z such that .99 of the area under the curve is less than z (to the left of z).

A: Introduction:The random variable, Z conventionally denotes the standard normal variable, which has…

Q: 2- Find the area f the negion cut from the trst quadrant by the regson r= l+ Sino?

A: From the given problem:   r=1+sinθ   Given first quadrant it means:   θ→0 to π2r→0 to 1+sinθ   Now…

Q: 87.49% of the area is below what value of z?

A: We have to find the z value below which the area is 87.49 %

Q: Find the area between y = 3 sin a and y = 7 cos a over the interval [0, 7]. Sketch the curves if…

A:

Q: TT Find the area that is bounded by r = sin 0 and lies in 2 3

A: Given Data The equation of a curve is r=sin θ The interval of θ is π/2≤ θ ≤ 2π/3   The expression…

Q: Find the area bound by y = 1, y = ln(x), x = 0 , and y = 0.

A: Let's find.

Q: 8 Find the area that is inside r=H+20in e and auturide rG - nin E.

A: To find: The area that is inside r=4+2sinθ and outside r=4+2sinθ. Calculation: First shade the…

Q: 12. Find the area inside the cardioid defined by the equation r = 1-cose.

A: Equation of cardioid given is

Q: Q-Find the area of the region that outside r= 2 sin (e) and insider (1+cos e)?

A: Given functions are r=2sinθr=1+cosθ These are plotted on cartesian plan using graphing calculator.

Q: The area under the graph of y = on , e] equals 1+ In2 Select one: O True False

A: we have to find integration

Q: Find the area under = 3 sin(x) and above y = 3 cos(x) for T < x < 2. (Note that this area may not be…

A:

Q: Find the area between y = x + 11 and y = 3x + 2 between x O and x 2. %3D |3D Enter the exact answer

A: Given:       y=x+11       y=3x+2 over interval 0,2 The area between curves is the area between a…

Q: Find the area bounded by the curve r= 2+cos θ

A: Given problem:- Find the area bounded by the curve r= 2+cos θ

Q: find the area enclosed by one loof of the curve of r = sin(4θ)

A:

Q: Bm 11 2元

A: we need to find the integral of the function in the given limits to get the

Q: Find the area of the region between  ?=sin(x)  and  ?=cos(x)  over  [2?/3,3?/4].

A: To determine the area between the two curves between the given limits

Q: Consider the value of t such that 0.01 of the area under the curve is to the right of t. Assuming…

A: Given Information Significance level =0.01 Degrees of freedom = 28 t-value = 2.467140098( Using…

Q: Consider this rose curve. r = 2 sin(60) a) How many petals does it have? b) Set up the integral for…

A: According to question, Given rose curve, r = 2 sin 6θ

Q: TT 10. Find the area that is bounded by r = sin 0 and lies in 2 3

A:

Q: 5. Use the concept of the definite integral to find the area of the region under the graph of y =…

A: we have to use the concept of the definite integral to find the area of the region under the graph…

Q: 29. Estimate the area under the graph in the figure by using (a) the Trapezoidal Rule, (b) the…

A:

Q: find the area bounded by r = 9 + 2 cos(θ)

A: Here given the equation of cardioid as Then the area inside the cardioid is defined as

Q: Set up the equation to compute the area inside the graphs of r = sin 0 anc r = 1 - sin 0

A:

Q: 3. Find the area in the first quadrant under the curve 1 y = 1+x

A:

Q: Find the area between the paral x = y? – 1 and x = 2y? – 2

A:

Q: Q2: Find the area common between the curves r = a (1+ cos0), r =a (1 – cos0).

A:

Q: Graph the curve and find the area that it encloses. r = 2- cos e

A: Given: r=2-cosθ

Q: Evaluate the integral and interpret it as the area of a region. 6 •π/2 19 sin(x) - 9 cos(2x) dx

A:

Q: Find the area under y 3 sin(x) and above 3 cos(x) for T < x < 2T. (Note that this area may not be…

A:

Q: Find the area between y = In x and the x-axis from x = 1 to x = 3. 3 In 3 – 3 In 3 3 In 3 + (-2) OD.

A:

Q: Graph the equations and shade the area of the region between the curves. Determine its area by…

A: The solution are next step

Q: Find the area between y = In x and the x-axis from x = 1 to x = 3. * 3 In 3 - 3 In 3 3 In 3 + (-2)…

A:

Q: (8) Find the area under the curve f(x) = e* – 1 from X =1 to x 2 Leave the answer with e, don't use…

A: SOLUTION-

Q: Find the area of the following: 1.y = COS X cos x and y = sinx [0,21]. on

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Consider the area between the graphs x + 2y = 29 and x + 6 = y?. This area can be computed in two…

A:

Q: Find the area that it encloses. r = 2 − 2 sin(?)

A: To find: The area that encloses r = 2 − 2 sin(?). Graph: The polar curve  over the interval [0,2pi]…

Q: 7. r a sin 3 e

A: Explanation: Given that,  r=asin3θ  Here we will put  r=0sin3θ=0⇒3θ=0 or π⇒θ=0 or π3

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.