Q1) Find only the limits of the integration of the figure below in the order (dx dy). 1-S[ dxdy x= 2-y R

Q: Find dy dx? if y= 5cos2x-4sin 2x at x =0

A:

Q: dy evaluate dx (sinx+1) 5-1f: y = (cosr+1)

A:

Q: Rewrite the integration in terms of u. 2x dx = du x² + 16

A: Given :∫032xx2+16dx

Q: Given F(x)=2f(xr)-8(x) and fS-1) = 2, f'(-1) = 3,9(-1) = -5,g'(-1) = 4, find F'(-1). %3D %3D

A: The detailed solution is given below Thank you

Q: . Integrate: [x7*dx

A:

Q: x3 for y = Differentiate. Find dx x-1

A:

Q: 4) Solve: x.[dy/dx] - y = x²sinx (Hint: Use the integrating factor).

A: Step 1: Step 2: Step 3: Step 4:

Q: 1- dX dy (bux> dy 2- dx : 2X Secy 3. (1-x"): - 2Y dy

A: Answer 1 -  As the cube root of 64 is 4, thus open the parentheses of the RHS of the differential…

Q: 12. Compute [ ft 2y Suggestion: Change the order of integration e-y/x dxdy.

A:

Q: 2. Integrate dy (a) Vy* +16 (b) |6x – x² dx

A:

Q: dy (1 + æ)* Find for y dx Ans=

A:

Q: (x² - 4) dx x² + 2x² + 2x S

A:

Q: X dy dx - Y 2 x arcsin (r)y5

A: CONVERT THE GIVEN EQUATION IN LINEAR EQUATION OF FIRST ORDER BY SUBSTITUTING v=1y4 AND THEN SOLVE…

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.