Use Property 8 of integrals to estimate the value of the integral. ∫20(x3-3x+3)dx.

Q: sech(ln x) dx リ-5

A: Given integral, ∫-50sech(lnx)dx The objective is to evaluate the integral by substitution.

Q: Find the integral ∫dx / 1+coshx.

A: We write the function using ex

Q: Use the table of integrals to find the indefinite integral. -dx 3-5x

A:

Q: Use integration by parts to find the indefinite integral.

A: Integration is the process of finding the anti-derivative function of the given function. The…

Q: Use a table of integrals to evaluate the definite integral.

A:

Q: Use a table of integrals to find the indefinite integral.

A: Use a table of integrals to find the indefinite integral.

Q: Use a table of integrals to evaluate the definite integral.

A:

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

A:

Q: Use integration by parts, together with the techniques of this section, to evaluate the integral.…

A:

Q: Use Property 8 to estimate the value of the integral.

A:

Q: Use properties of the integral and the formulas in the summary to calculate the integrals.

A: Given : ∫25x2dx

Q: Use a table of integrals to find the indefinite integral

A:

Q: Use Property 8 to estimate the value of the integral.

A: Given:

Q: Use the Table of Integrals to evaluate the integral.

A:

Q: 4 dx x4-1

A:

Q: Approximate the integral from 2 to 14 (x2 -5)dx using 4 rectangles

A: To find the area under the curve using rectangles, the Reimann sum is used.First, we need to find…

Q: Evaluate the integrals ∫8 cosh √x/√x dx

A: We have to evaluate ∫8coshxxdx Let substitute t=x dtdx=12x2dt=1xdx Substituting the above value in…

Q: Evaluate the integrals using integration by parts. ∫ x sin x cos x dx

A:

Q: Use the properties of integrals to evaluate integral 0 to 1 (4+3x2 ) dx

A: Given: I=∫014+3x2dx for evaluating given integral, first we separate terms then integrate it

Q: 5 .Use the definition of the integral to evaluate | (2x - 3)dx

A:

Q: Find the integral of (x)(arctan x) dx,

A: Given: evaluate

Q: Use a table of integrals to find the indefinite integral ∫ 1 /(x2 + 4x + 8) dx

A: Consider the given integral ∫1x2+4x+8dx

Q: Use a table of integrals to find the indefinite integral. (Reme 7 + 9x2 dx

A: method :-   I use Trigonometric substitution method to solve the given integral

Q: Evaluate the integrals using integration by parts. ∫x2 sin x dx

A: Given: ∫x2sinx dx

Q: Use a table of integrals to find the indefinite integral ∫√x arctan x3/2 dx

A: The given integral is I=∫xtan-1x32dx. Concept used: By part of integration ∫udv=uv-∫vdu Calculation:…

Q: Given that x² dx = use this fact and the properties of integrals to evaluate (6 – 3x2) dx.

A:

Q: Use a table of integrals to find the indefinite integral ∫ 2 / x3√(x4 − 1)   dx

A: Use a table of integrals to find the indefinite integral ∫2x3x4-1

Q: Evaluate the integral, if it exists.    ∫ (8 x3  +3x2) dx

A: Given- ∫8x3+3x2dx To evaluate- The above integral. Formula used- The power rule, ∫xndx=xn+1n+1+C,…

Q: Evaluate the integral.  integral x2 /sqrt (x+1)  dx

A: Given I=∫x21+xdx

Q: Evaluate the integral.

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 1- 36x2 dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) √3x√1- 3x√ 1 - x4 dx

A:

Q: Evaluate the integrals using integration by parts. ∫x3 ln x dx

A: the given integral is: ∫x3lnx dx we have to evaluate the integral using integration by parts. lnx is…

Q: Evaluate the integral of [(dx)/(x2)(sqrt(x2-1))] dx

A:

Q: Evaluate the integral using integration by parts where possible. (Use C for the constant of | (x2 -…

A:

Q: Use a table of integrals to find the indefinite integral

A: ∫1x22+9x2dx Put, x=2tant3⇒dxdt=23sec2t⇒dx=23sec2t dt

Q: .2 32. 8x dx, x > 8 -

A:

Q: Evaluate the integral x2 cosh 2x dx.

A: Given:

Q: Use the Table of Integrals to evaluate the integral.  ∫01x4e-x dx

A: Given:∫01 x4 e-x dx∫u dv=uv-u'v1+u"v2-u'''v3+u''''v4-.......

Q: Use a table of integrals to find the indefinite integral ∫x arccsc(x2 + 1) dx

A: Consider the given integration as ∫xcsc-1x2+1dx

Q: -1Vx X. dx Vx cos

A:

Q: Use a table of integrals to find the indefinite integral ∫ e3x /(1 + ex)3 dx

A: Use a table of integrals to find the indefinite integral ∫ e3x /(1 + ex)3 dx

Q: Evaluate the integral, if it exists.

A: Given: An integral ∫03|x2-4|dx x2-4>0, for x≥2 x2-4<0 for x<2 Thus,…

Q: Evaluate the integrals ∫sinh 2x dx

A: Given: ∫sinh2xdx

Q: 2-V1-x dx by interpreting the integral in terms of area. -

A: ∫-112-1-x2 dx On simplification, we get ∫-112-1-x2 dx=∫-112 dx-∫-111-x2 dx   →1 Now consider, ∫-112…

Q: Evaluate the integral by using u-substitution and changing the limits of integration. x3 dx -1 ex*+1

A:

Q: Evaluate the integral. (Use C for the constant of integration.) dx 49 - x2

A: We have to find the integral

Q: Given that dx use this fact and the properties of integrals to evaluate (5 – 9x2) dx. =

A: This can be evaluated as follows:

Q: 3+ In(2x) dx 00 X-1 1

A:

Q: Use Property 8 of integrals to estimate the value of    ∫13 √ (x2  + 3 ) dx

A:

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.