Match the integrals in the left column with the correct evaluation method in the right column. Using integration by parts u-sin) aax Using integration by substitution utanx) Using integration by substitution u-sec) Using integration by parts usec) avtarudx D. Son war Using integration by parts u-1 av-sin) ax Using integration by substitution u-sn)

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: The exact value of the integral [In[I + x) x²]+ 2dx is-0.3521. Evaluated this integral (a) by the…

A: (a)∫12x-x2+lnx+1+2 dx using n=4 trapezoids.The trapezoidal rule states…

Q: d. Integrate your integrals from parts c and d and show that the two integrals give the same area.

A: Given equations are: y=x2 and y=4 The integral representing area bounded by two equations with…

Q: (3, 1) (у? + 2ху) dx + (- 1, 2) (x² 2ху) dy +

A: We have to show that the curvilinear integral is independent of path and we have to find its…

Q: / 1 – x2 dx (c)

A: Given I = ∫1-x2x3dx    ......... (1) Integration by parts ∫u(x).v(x)dx = u(x)∫v(x)dx…

Q: The region of integration in the integral 2x So So a f (x, y)dydx is rectangle Select one: True…

A: The region of Integration in the integration in the integral  ∫02 ∫02x F(x,y) dyd2  is a rectangle…

Q: Use integration tables to find or evaluate the integral.

A: We have to evaluate the integral: ∫x4+5x2dx Assuming, t=4+5xx=t-45 Differentiating,…

Q: By using double integrals, find the area of the regions enclosed by a) curves y = y=-x², lines x =…

A:

Q: Evaluate the integral by making an appropriate change of variables. / 9 sin(49x2 + 64y2) dA, where R…

A:

Q: Use the Fundamental Theorem of Line Integrals to calculate exactly. F-6 sin(ox +)+ sin(6x )j along…

A:

Q: By using double integrals find the area between x = – y², lines y = x – 4, y = -2 and y = 2.

A:

Q: how to solve problem in photo attached

A: The given integral is,

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 16 +…

A: Integration by parts:∫uvdx = 4∫vdx - ∫[ddx(u)∫ vdx]dx

Q: Use integration by parts to evaluate the integral: fin(2) - V/="da = ,11

A:

Q: Use double integrals to find the area inside the curve r = 5sin(e)

A: The given curve is:

Q: ind the integral using integration by parts. Do not use a table of ntegrals. ze -dz

A:

Q: Evaluate the integral using integration by parts where possible. r In(8r)dx

A:

Q: Use integration by parts to compute the integral S xsin(4x)dx and Inx dx

A:

Q: Find average Value of f(x)=X³ on [1,2]. Then find Point CE [1,2] meun € [1,2] quaranteed by the…

A:

Q: Evaluate the integral using integration by parts with the indicated choices of u and dv: -6t sec2…

A: Given integral is : ∫-6tsec2tdt=-6∫tsec2tdt

Q: Use the methods of (1) left Riemann sum, (2) right Riemann sum, (3) trapezoidal rule, (4) parabolic…

A: According to our company's guidelines I can only answer first three subparts of the question since…

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

A: The solution is Given as

Q: Evaluate the integral by making an appropriate change of variables.   8 sin(81x2 + 81y2) dA,   R…

A:

Q: Use the Fundamental Theorem of Line Integrals to calculate 7. di exactly. F6 sin(6x + y)i + sin(6x +…

A:

Q: By using double integrals, find the area of the regions enclosed by: (a) y=4-x² and y=3x (b) y=sinx…

A: Area of region between two curves.

Q: Evaluate the integral by using a substitution prior to integration by parts. Sin(2x+2x²) dx Hide…

A: Given ∫ln2x+2x2dx

Q: Use geometry and properties of integrals to evaluate

A: Given integral is ∫15 x-2+-x2+6x-5dx. The above integral can be written as below. ∫15…

Q: 3. V1-x². /1 — х2 хdx

A: To solve this integral, a substitution is made. The substitution taken is 1-x2=u. This equation is…

Q: 1. Sketch the region of integration for integral by reversing the order of integration. I'sin (y)…

A: Hello, thanks for your question but according to our guidelines I am answering the very first…

Q: Given that x2 dx use this fact and the properties of integrals to evaluate (2 - 3x2) dx. %3D

A: Answer is- 1 Explanation is given below...

Q: Find the approximate integral of 4 1 * -dx In x 2 when n=10 using a) the Trapezoidal Rule, b) the…

A:

Q: Evaluate integral using integration by parts. Se- 50 sin 150 d0 Se -50 sin 150 d0 = %3D

A: Apply the integration by parts two times and simplify.

Q: (b) 3 – cos(x) 2

A: Follow the procedure given below.

Q: Use comparison properties of integrals to make a conclusion about the lower and upper values of ,…

A:

Q: What is the value of the approximation of the integral So (1 - e-2) dr using four-segment…

A: Using the formula  ∫abf(x) dx ≈b-a2n[ f(a) + f(b) + 2 ∑i=1nf(a+ih) ] where h = b-an,  n = number of…

Q: Evaluate the integrals by using a substitution priorto integration by parts. ∫z(ln z)2 dz

A: Since, we have to evaluate the integral given below:-∫z(ln z)2dz -(i) using substitution and…

Q: Consider a volume of a solid under the surface z = sin(x³) can be denoted as 4 2 sin(x³) dx dy i.…

A:

Q: Use integration by substitution and/or by parts to compute the integral Jx In (5 +x)dx .

A:

Q: 1,125 ! 1 dx 1+2x

A:

Q: 12x CO

A: Given,          ∫512x2cos8xdx

Q: Evaluate the integrals using trigonometric substitution dz 2² √2²-4

A: Find the inegrals by Trignormeric substitution

Q: Evaluate the integrals using integration by parts. ∫(x2 - 2x + 1)e2x dx

A: To evaluate ∫x2-2x+1e2xdx

Q: use a double integral to find the area of the shaded region.

A: The figure is symmetrical about both axes. Therefore, initially the area of the shaded region in…

Q: 6. Evaluate the intergral | (2x + V4 – x²) dx by using the properties of integrals and your…

A: Given: ∫-22 (2x+4-x2 ) dx To find: Value of the integral.

Q: Use the substitution formula to evaluate the integral. the integral from 0 to pie/2…

A: To  Determine:Use the substitution formula to evaluate the integral. Given: we have an integral…

Q: In The value of the definite integral flm 12 √ex - 9 dx is in the form F(b) - F(a), where a JIn 9…

A: To evaluate: ∫ln⁡9ln⁡12 ex−9dx Let I =∫ln⁡9ln⁡12 ex−9dx Given: ∫ln⁡9ln⁡12 ex−9dx = c3-dπ Let ex−9=…

Q: Evaluate the integral by making an appropriate change of variables. 7 sin(25x2 + 25y²) dA, where R…

A: Double integral evaluation, conversion to polar coordinates

Q: Solve the integral by two grid in the y-direction and four grid in the x-direction with Trapezoidal…

A: The given integral is: ∫45∫23xcosydydx Here  x0=4, x1=5y0=2, y1=3fx,y=xcosy By Trapezoidal rule,…

Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.) 9 sec²…

A: This question can be solved using the concept of integration by substitution.

Q: 1,125 1 - dx 1+2x

A: We can solve this using formula of 3/8 rule and 1/3 rule of simpson

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.