integral -{cay,a> 91-) Evoluate te nplhas)ss - 24x<0, Ocyc1, -16241} . where

Q: 10. Prove by using integration by change in variable the ff. integral: dx :du 3D arcsecх+ С xVx2 – 1

A: We have given the integral ∫dxxx2-1 = I(say)     Put   x2-1 = t   ⇒x2= t2+1     Differentiate w.r.t…

Q: 4. Water is to be pumped from the top of a cylindrical tank with radius 3m and height 10m. The tank…

A: To find: The expression for pumping water from the top of the horizontal cylindrical tank of length…

Q: tan (x) sec²(x) dx.

A:

Q: Use Green's Theorem to evaluate the line integral

A:

Q: What is the integrable form of sin-cos-sino de? 2 2

A: Integration

Q: Show that arctan(Tx) – arctan(x) -dx In T. by first expressing the integral as an iterated integral.

A: To show

Q: Each integral represents the volume of a solid.Describe the solid.   ∫0π/42 π (π - x) (Cos x - Sinx)…

A:

Q: dydx ctan x Jo Ji 1+ y²

A:

Q: region bound by y=x2 y=2x and y=3, rotated about x=-1, set up the integral using washer method,…

A: Graph the bounding region and the axis of rotation. Since the axis of rotation is a vertical axis,…

Q: Find the integral. Show complete solution. sinx -dx 1+sinx 3.

A: NOTE: You posted multiple questions, we have given an answer to the first question, if there is a…

Q: write the Sum of the 2 Pterated integrals ntegral by converting to porar coordinutes Eraluate the…

A: Draw the regions from given limits of integrals and find the limits of added region as shown in…

Q: triangle with vertices (-4, 1) (-2,1) (-3,2), rotated about x=1, set up the integral using the shell…

A: Given vertices of triangle are (-4,1) (-2,1) (-3,2) &amp; axis of rotation is x=1 we have to find…

Q: 8 Evelluate the double integral: + 3x) dydx

A:

Q: sec² 0 de. 1- tan 0 Evaluate the improper integral:

A:

Q: Сompute L f dx, where f(x)=|x|.

A:

Q: Use IBP to evaluate the indefinite integrals. 1. ∫ x³sin x dx 2. ∫ sec³ x dx 3. ∫ x cot² x dx

A:

Q: 3 Find tue Inde finite intyrel 2C In (x") doc at

A:

Q: Givm trapgoidal rule with h =0.25 by Using apploximate the integral.

A: The solution is Given as

Q: The base of a three-dimensional figure is bound by the line y = 4 sin(x) on the %3D interval [0, 1].…

A: Consider a vertical cross-section of the required solid with thickness, as shown below: The volume…

Q: S Vtan x sec“(x)dx Evaluate the integral a

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: use in tergration by parts to solve

A: Given,  ∫012xcosπxdx  We have to find the integral using integration by parts.

Q: If a force of 128 lbs is required to stretch a 10-ft spring by 4 ft. How much work is done by…

A: Here we have to use the concept of integral calculus

Q: FIND THE CENTROID OF THE REGION IN THE FIRST QUADRANT BOUNDED BY THE GRAPH OF y=9-x2, THE X-AXIS,…

A: Given region is bounded by the graph of  y=9-x2, The X-axis and Y-axis

Q: Use integration by parts to obtain the formula dr. sarating Invorc of Funotiono

A: Given:∫1-x2 dxIntegration formula:∫sinx=-cosx+C∫xn dx=xn+1n+1

Q: 7. (x² - 2x + 3)dx 5²

A: SOLUTION-

Q: volume of solid of as revolution y^2=4x and x^2=4y about the x axis

A:

Q: Verify the integration formulas in Exercises 38. sechx dx sechx x =

A: Integration properties and methods help to find the required function after the integration.…

Q: 1- 3 sin (x) dx. 2 cos2 (x)

A: Computer the Integral

Q: What is the integrable form of sin-cos-sino do? 2 2 u² – 1 du 2 | cosu du 1- u? du -2 | sinu du

A:

Q: 5x'/1 – x² dx

A: Given: I=∫015x31-x2dx For evaluating given integral, we substitute x=sinθ…

Q: line integral Compute the where part of the cirele x² +yR=9 C is the %3D in the first quarant from…

A:

Q: How do Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem relate to the Fundamental…

A:

Q: Evaluate the integral. sec do %3D

A: According to guidelines we are supposed answer only first question if you want any particular…

Q: TRUE OR FALSE? The given line integral is independant of path.

A: The given line integral is ∫C2xz3+6ydx+6x-2yzdy+3x2z2-y2dz Compare the above line integral with…

Q: * Using integration by parts, the integral sec³dx is equal to 1 1 - secxtanx +In|secx +tanx| + C 2 1…

A: Use by parts method of integration

Q: Show that the integral is independent of the path, and use th Fundamental Theorem of Line Integrals…

A:

Q: The region is bounded by the graphs of the equations y sin x, y = 0, x=0, and x-A. For the…

A: See this solution in below

Q: Give examples of basic integration using reciprocal rule

A: Reciprocal rule of integration: ∫1xdx=lnx+C

Q: segment from ( 0,3,0) to (1, 3,7).Use line integral and check answer by caleulating (s.y.)

A:

Q: What is the surface integral in m2 of a long thin wire with circular cross section, length…

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Q: Integrate: (7x³ + 4x²) dx

A:

Q: EQUへTION (+2x?) AS A (40MOGENEOUS DIFFERENTIAL Ē QUATION SHOW TYAT AND MAKE AN APPROPRIATE…

A:

Q: How are triple integrals defined in cylindrical and spherical coor-dinates? Why might one prefer…

A:

Q: Compute the volume of the solid obtained by revolving the graph of the function f(x)= 9x5 on the…

A:

Q: integral of sec^4 (x) tan^2 (x) dx

A: Definition used -                                sec2x=1+tan2x…

Q: Compute the volume of the solid obtained by revolving the graph of the function f(x) = 8x³ on the…

A:

Q: sin-cos-sino do? 2 2 What is the integrable form of

A: Given that,

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.