Solve the integral. dx 6. J1- 4e2x

Q: z° + 12z2 dz z6 + 8z3 + 41

A: Solve the integral:  ∫z5+12z2z6+8z3+41dz=16∫dz6+24z3+41z6+8z3+41…

Q: Calculate the value of 102 – 101 correct to four significant figures.

A: Given that  √102-√101

Q: Find the integral.

A:

Q: A tank is full of water (see figure). Find the work required to pump the water out of the spout (to…

A:

Q: sec? x dx 11. V50 – sec? x

A:

Q: 2x ०5+.a

A: We use substitution method to solve this integration

Q: Evaluate the definite integral.

A:

Q: Evaluate the integral and explain each Step. े्यकिण

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 2. Solve For O40127 4cose=CO50+3

A: The given equation is;  4cos(theta/2) =cos(theta) +3.

Q: V9x2 + 25 1. r2

A:

Q: S 4e²x-1dx

A:

Q: 2e-2x – 3e3x 14. - dx e-2x + e3x

A: deaxdx = a.eax ∫1u du = lnu +C

Q: Evaluate the integral. 49 9Vx dx J25

A: Given: I=∫25499xdx we know that ∫xndx=xn+1n+1+c

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A: Given :-Areas A1=5 , A2=3,A3=2, A4=1

Q: r5 [² (2² 2. √2 (2x² – 3x) dx

A:

Q: Solve the function 3x4ex^5 dx on the integral from 2 to 3

A: Given:

Q: 383. dx (x² + 1)?

A:

Q: Intesrate ナhレ ex pressi

A: Given integration is : ∫4x+5dx To find the value of integration.

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.