DETAILS AlL LARCALC11 2.5.503.X d'y Find in terms of x and y. xp 2. 14x = 5 d²y

Q: x²-x dx [x -] %3D

A: Given,

Q: Differentiate the function below. y= (x2 + 4) (x² – 2) 8 d [(x? +4) (x² - 2) ® _ = O %3D dx

A: Ans is given below

Q: dx 2+x?

A: Given, ∫dx2+x2 We have to integrate it.

Q: dx 6. 4+ 5сosx

A:

Q: Integrate the function. dx XV 49x -4

A: Given: Let I=∫dxx49x2-4 To Find: To integrate the given function

Q: dx Vx+ Vx

A: Given: ∫x-x3x3+x4dx

Q: Find ∫sec2 (5x + 1). 5 dx.

A: we have to find the value of the given indefinite integral. ∫sec25x+1·5dx

Q: .2 dx 6. (x-1)3

A:

Q: X arccsc(x- + 13) dx 6. 10

A:

Q: dy Find for y = x(4x + 3) dx - |3

A: The function is given by y = x4x+313 To evaluate : dydx

Q: x V2x – 1 dx dr

A:

Q: Evaluate.

A:

Q: Dsinx-sin3x [3] sin³x = find D and E. %D E

A: Solve for D and E

Q: dx 19. S 2-x

A: Given: ∫dx2-x

Q: .2 x² arctan(3x) dx %3D

A:

Q: what is y=1/2tan3x

A:

Q: Eveleate inter ssin(2x) dx

A: We can find the integration as below.

Q: dx 28. 1– x4

A:

Q: .5 X° +2x -Xp- X +1 -3 X° + 2x -dx%(Simplify your answer.) %3D X +1 3.

A: Consider the integral

Q: 8 .3 X (1+x)5 - dx

A:

Q: 9 coshx - 5 sinhx 15 %3D

A: To solve  9coshx-5sinhx=15

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.