Q4. Evaluate the integral / V1- dr.

Q: ,2 2. 6+t dt

A:

Q: Find the indefinite integral. Vx +2 -dp- 3 X,

A:

Q: -s(-+)( + }) 1. dt

A:

Q: dx T² + 4 2

A: We have to find value of indefinite Integration.

Q: dy y/ 9y2–16

A:

Q: Evaluate the integral. 7y 1-7y dy

A:

Q: Evaluate the integral | 3 dx. V9x -4

A:

Q: Evaluate the integral dx (2x + 11) by making the appropriate substitution: u =

A:

Q: Evaluate the definite integral. 4 dz V7z +8

A: Using definite integral

Q: Calculate the indefinite integral 13 – 7t² – t + 43 dx. - - t2 – 4t – 12

A: Given:

Q: V3 – x² dx

A:

Q: Evaluate the integral. x sec2(8x) dx = +C

A:

Q: 1= [3y/7-3y° dy

A:

Q: Evaluate the integral.

A: Given integral to evaluate ∫14x249-x2dx=14∫x249-x2dx substitute u=sin-1x7x=7sinudx=7cosudu The…

Q: Evaluate the integral. (2 + 2y)? dy

A:

Q: Which integral could be evaluated using the substitution u = x ?

A:

Q: Express the integral Js(x) dx in terms of Jo, J1 and J2.

A: Bessels function identity:  Jn+1(x)=2nxJn(x)-Jn-1(x) Given: ∫J5(x)dx

Q: Evaluate the integral. 4x° V1 – x² dx = 0, NOTE: Enter the exact answer.

A: Given: Let I=∫01 4x31-x2 dx To Find: To evaluate the given integral.

Q: Evaluate the integral. (x6 + 4y³) dy

A:

Q: Find formulas for the functions represented by the integrals.

A:

Q: Evaluate the integral v22 -6x? dx V1- x2

A:

Q: Evaluate the integral. 4 | VE(6 + 2t) dt

A: use distributive property on function and integrate it.

Q: V3 d) dr VT² + 1

A:

Q: Estimate the value of the integral 4- x²y2 dA, S = {(x,y)| x² + y? 0} |

A:

Q: 4 + V16-x? dx 3 2

A:

Q: Evaluate the integral 35 dz 4 by making the substitution u = x* – 6. +C

A: integration

Q: Evaluate the integrals

A: Consider the integration as I=∫01x2+xdx

Q: Evaluate the integral 13t – 5| dt.

A:

Q: Find the complete integral of (p2 + q2)y = qz.

A:

Q: | 3t°(t° + 2)*/² dt 8. 3/2

A:

Q: 15. S(x + 2)²dx

A: Solve the following

Q: valuate the integral ∫x2/x3+1dx using an appropriate substitution.

A:

Q: Evaluate the integrals

A: Evaluate∫−π3−π44sec2t+πt2dt

Q: Evaluate the following integral. ∫ 2z5e1-z dz

A:

Q: Evaluate the integral. V19 12) x dx 1

A:

Q: Evaluate the integral.

A: We have to evaluate the integral: ∫x3xx2+3y2dy Here we have to integrate with respect to y so x2…

Q: Evaluate the integral: dx V4 – x2 Jo

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

Q: Evaluate the integral. Clearly indicate u-substitution steps if required. 19 J2+ 5y

A: Given integral is ∫195+2ydy evaluating the integral with u substitution

Q: Evaluate the integral: 9e3x dx е3x Vебх — 25 -

A:

Q: | Va (2 – x)° dx 1

A:

Q: Evaluate the integral x³ + 76 J dx. x2 + 5x + 4

A:

Q: Evaluate the integral. (x8 + 6y5) dy

A:

Q: To evaluate the integral/ V3 – 3x² dx,

A: Substitute, x=sin(θ)dx=cosθ dθ The expression f(x) becomes,

Q: Evaluate the integral. x sec (8x) dx + C

A:

Q: Evaluate the integral.

A: Evaluate the integral.              ∫04-x2x2ydy

Q: Evaluate the integral |-1|2 – 4z| de

A:

Q: Evaluate the integral. V3 dx 1/V31 + x2

A: Consider the given integral: ∫13331+x2dx Now let , x=tanudx=sec2u·du If, x=3   Then,…

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.