+o0 1 dx J2 æ Va2 – 4

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A: To evaluate the integral∫0∞x3(x2+1)2dx

Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. у dy V4-y?

A: Now consider,

Q: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate…

A:

Q: Determine whether the improper integral converges or diverges. If it converges, determine the value…

A:

Q: +o0 3 dx — 16 .2

A: The given integral is, I=∫7∞3x2-16dx Solve the integral as, I=3·∫7∞1x2-42dx Consider the formula,…

Q: state whether TN or MN underestimates or overestimates the integral and find a bound for the error…

A:

Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answe dx = (x +…

A:

Q: Find the integral for f dx when n-4 by using Trapezoidal rule for five digits

A: Using  trapezoidal rule,Area=h2y0+y4+2y1+y2+y3Let fx=xx2+2, where, h=b-an=2-14=0.25          a=1,…

Q: Evaluate the integral. If the integral converges, determine the number it converges to. If the…

A:

Q: Explain why the integral is improper and determine whether it diverges or converges. Evaluate the…

A: Given

Q: Determine whether the integral is convergent or divergent. 1 dz z2 + 3z + 2 convergent divergent If…

A: ∫0∞1z2+3z+2dz

Q: Determine whether or not the infinite series below converges.

A: Divergent test: If

Q: r0o VInx dx 2

A: Consider the given integral ∫2∞lnxxdx

Q: 3. Determine whether the improper integral is convergent or divergent. Do not guess! y2 dy 0- y6+ 9

A:

Q: 2x dx Vx² – 1 2 1 8

A:

Q: Evaluate the integrals that converge, enter 'DNC' if integral Does Not Converge. 7xe dx =

A:

Q: Evaluate the improper integral if it converges. (If the quantity diverges, enter DIVERGES.) -1 8 dx…

A:

Q: 星() ()y点r

A: We will use the bounded convergence method to show that the given integral is convergent.

Q: determine whether the doubly infinite improper integral converges and, if so, evaluate it.Use…

A:

Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer.

A:

Q: Evaluate the improper integral. If the integral converges, enter what the integral converges to. If…

A: Evaluate the improper integral as, I=∫5∞e-xdx=-e-x5∞=-limx→∞e-x-e-5=-0-1e5=1e5=0.006738

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it converges

A: The given integral is ∫4∞1xlnx3dx.

Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. dx = %3D…

A: Given that, ∫-∞1e2x1+e2xdx Let,  u=1+e2xdu=2e2xdx For x=-∞, u=1+e2(∞)=1+0=1

Q: Determine if the improper integral converges or the integral. diverges. If it converges, evaluate dz…

A: Calculate the improper integral of the given integration. The integration is given as: ∫−2∞ 14+z22dz

Q: thi Prove that the improper integral } ] docdy (1 + x² + y²) ³¹²/₂ Converges

A:

Q: Determine whether the integral is convergent or divergent. The integral from negative infinity to 0,…

A: Given: I=∫-∞0zz4+81dz                                                                        ..1

Q: Which of these improper integrals is convergent? e dz 1 eda e*dx 3 -dr 3 -dr 3 8 8

A:

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

A: Here we have to check the convergence of integral.

Q: Evaluate the integrals that converge, enter 'DNC' if integral Does Not Converge. 8. dx

A: To evaluate the integral ∫018x3dx  Concept used: Power rule of differentiation. ∫xn=xn+1n+1+c

Q: Explain why the integral is improper and determine whether it diverges or converges. Evaluate the…

A: The given integral is:

Q: Determine if the following improper integral converges or di- verges. If it converges, find the…

A: As per the guidelines only one question should be solved. Thus repost the second different question…

Q: 1 dx ° 5 2x + 1

A:

Q: Show that the integral is either Convergent or Divergent. If it is convergent evaluate the integral.…

A: Given Data The integral is      Using the limit to show the integral is convergent or divergent,…

Q: Determine whether the integral is convergent or divergent. Evaluate from −∞ to 0. z/z^4 + 81 dz If…

A: We need to find if series converges or not.

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: The given integral,                ∫-∞182x-32dx

Q: Determine whether the following integrals converge or diverge. If they converge, find the value of…

A:

Q: J. xinx) dx converges and evaluate the integral in those cases. Determine for what values of p the…

A: Consider the equation

Q: Evaluate the improper integral. If the integral converges, enter what the integral converges to. If…

A:

Q: Evaluate the improper integral ∫∞0ectdt∫0∞ectdt. For what values of c does this improper integral…

A: The given improper integral is

Q: Evaluate the integrals that converge, enter 'DNC' if integral Does Not Converge. 3 , da = x2 – 9 -

A: Given query is to find the value of the integral.

Q: Determine whether the improper integral converges or diverges. If converges, find the value. In x?dx

A:

Q: 8. -y/2 dy J4

A: Given integral, ∫4∞e-y2dy

Q: luate the integral if it converges and he integral diverges, indicate that us dx x2 The integ

A:

Q: 13 1. x dx, n = 3 3D3 n%3= 1

A: Find the average of the limits to obtain the width of the rectangle. ∆x=13-13=123=4 find the values…

Q: Evaluate the integrals that converge, enter 'DNC' if integral Does Not Converge. -x2 2xe dx

A: Given integral  ∫0∞2xe-x2dx We have to find integral for converges or diverges.

Q: 1 Js V2x + 1

A: Given : ∫5∞12x+1

Q: Find the value of P which the integral Converges, absolotely Condition ally. Cosx dx

A: Given: ∫1∞cosxxpdxthis integral  converges,absolutely conditionally.

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it converges

A: Improper integral: ∫2∞ 1x3dxAt first we need to find,∫1x3dx=x-3+1-3+1+c=-12x2+c

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.