Problem 3. (3 points) The graph of ƒ is shown below. Evaluate each integral by interpreting it in terms of areas. 1. "N(x)dx=4 S² 0 5 de-11 dx 2. Så f(x) dr 3. 7 S" f(x) f(x) dx = 0 4. f(x) dx = [ S 0 10 Note: You can click on the graph to enlarge the image. 100 -1 1.0 18

Q: X-1 (x - 2)² 5. S dx

A: We have to evaluate the integral.

Q: x² dx %3D Use right endpoints and = 10 rectangles to find an approximation of

A: Given, Use the endpoints and n= 10 rectangles

Q: dy 80. VI + x dx xay + x. %3D

A: Given: 1+x3dydx=x2y+x2

Q: dx 5. S- (4x – x2)°/2

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find ∫√(2x − 1) dx.

A: Given:

Q: 2. (a) Define what it means by for y = f(x). %3D

A:

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: O Below are the graphs of functions p(x) and q(x). p(x) q(x)

A: here we have to carefully observe the graph and then answer accordingly to the questions asked.

Q: Encounter the sector's area beneath the diagram of f(x) to the right of x = 12. f(x) = 1 / (x - 9)2

A:

Q: If y = 9csc²-x 3 O -18 csc2> 3 -6 csc²}x• 3

A: Given: y=9csc213x

Q: Differentiate the function. y = (3x- 1)* (4 - x5) 3 dy dx II

A: To differentiate the given function:

Q: Find an equation of the line tangent to the graph of y sin x – 3y = 4 at the point %3D (, 4) .

A: y2sinx - 3y = 4 at (π/2 , 4) we have to find slope of function 2ysinx(dy/dx) + y2cosx -3dy/dx = 4…

Q: ۱۴ 14 g 3 3+1x 1= x² + 1× AND -FIND /dx WHEN X=2 =6.

A:

Q: 1 x² +5 -dx 3√x

A: We need to find ∫x12+5x3dx

Q: 4 S. x* - 6 dx = 14

A: Let, I=∫x4−6x14dx ⇒I=∫1x7x4−6dx ⇒I=∫x2x71−6x4dx ⇒I=∫1x51−6x4dx

Q: 3. x² - x dx =? %3D [x-1]

A:

Q: Væ – 4/x dx

A:

Q: Differentiate the function. R(a) = (6a + 1)² R'(a) = 12 X

A:

Q: n/2 1 If cotn+5x csc?x dx = then K=...... п/4 n+k

A: given that                                                    ∫π4π2cotn+5csc2x dx=1n+k now…

Q: - 1²/₁8 == // 1. On the curve of y = xe-2xa tangent line is drawn at the point where x = - This line…

A:

Q: 1/2 4 dx VI - x

A:

Q: 34 dx (г - 2)4/5 (x)

A: