f' (x) h' (x) 1)(x³ 3x) — (а? — 1)(23 — За)0 os (2 — За?) = x COS

Q: Given the curve X = 2y – y' and the line X = 0 Find the abscissa of the centroid X of the region…

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Q: antiderivative of y=xex

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Q: Romberg integration for approximating f(x) dx gives R = 1 and R22 = 12 then f(0) = 14 17 O 5/2

A: Consider the given: R21=1  and R22=12a=-1 and b=1

Q: Let f(x, y) = (/x+ y)e, + (/x– y)ez = ue, + ve, defined for |y| < x. The inverse is f(u, v) = xe, +…

A: We have to find x and y from the given relations.

Q: Transforming a square Let S = {(u, v): 0 ≤ u ≤ 1, 0 ≤ v ≤ 1} be a unit square in the uv-plane. Find…

A: Given: S=u,v| 0≤u≤1, 0≤v≤1 , T: x=u2-v2 , y=2uv. To find an image of S in XY-plane.

Q: On a map, 4 cm represents 2.5 km. If the distance between town A and town B on the map is 6.4 cm,…

A: The Scale of a Map: Ratio between the distance on the paper and the actual distance on the ground is…

Q: Reverse the order of integration I f(x, y)dydx.

A: The limits of integration have a critical role in evaluating a double integral. Usually, the upper…

Q: Let R be the region bounded by the graphs of y = VE, y = e, and the y-axis.

A: we have, y=x, y=e-x and the y-axis. y-axis ⇒x=0 Now, x=e-x logx=loge-xlogx=-xlogx+x=0⇒x≈0.4263 and…

Q: Proof IP A SD and Dis olosed. Then A' D

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Q: -x ôx ô -0, ây for z = tg(xy)+. y

A: Prove that for z=tgxy+xy, x2∂z2∂x2-y2∂z2∂y2+x·∂z∂x-y·∂z∂y=0.

Q: If U is the set of the numbers on a 6- sided die and B is the set of numbers on a 6-sided die that…

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Q: dy 1+e2 4. e"(1+x²) - 2x(1+e) = 0 ( Ans: = C) | 1+x2

A: We have to find

Q: Use the Trapezoidal rule to compute the work done in KJ. Work is given by = [ Pav PdV W = Pressure…

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Q: Show that if gcd (a, y) = 1 and a \xy Then a \x

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Q: Fir SO the YOUR TURN 1 Find an antiderivative f(x) = 8x7. %3D the Sup in y SOL

A: Given, f(x)=8x7 The antiderivative of f(x) is

Q: Changing order of integration Write the integral ∫20 ∫10 ∫1-y0 dz dy dx in the five other possible…

A: Consider the provided integral,

Q: When getting the points from symmetric equation, do we just do x = x0 or we have to divide it by x =…

A: To find the vector ,parametric and symmetric equation of line passes through point  and parallel to…

Q: NTEGRATE THE FOLLOWING (use integration techniques) - S sin rsin4rdx

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Q: BY GI Evaluate, F(r) C of the region / I,F = [y, -x

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Q: Consider the following consumer function: соnsumption, В, + Bzlncome, + u, uz = Income, Vi v ~ (0,…

A: Reviewing the information, given, consumptiont=β1+β2 Incomet +utwhere,ut=Incomet νtνt~0,σ2

Q: If divF (x, y, z) = 0 for all (x, y, z), then curlF (x, y, z) = (0,0,0) for all (x, y, z).

A:

Q: Approximating r In rd.r by Simpson;s rule, we get 1.5886 7.3540 3.2104 2.9470 0.6365 O

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Q: Surface area Find the area of the surfacer(u, y) = (u + y)i + (u - y)j + yk,0 ≤ u ≤ 1, 0 ≤ y ≤ 1.

A: Solution: Consider the given surface is : r(u, y) = u+yi + u-yj + yk0≤u≤1, 0⩽y⩽1 Now, find  ru × ry…

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.