The following integrals calculate areas of regions in the xy-plane. Say what shape each integral gives the area of. Be specific; for example, if the shape is a rectangle, give the base and height of the rectangle. Include a sketch of the region, showing the variable of integration, an arbitrary slice, and any other relevant quantities. a. ∫ 3xdx
b. ∫ √15-y^2dy
c. ∫ √81- x^2 dx
d. ∫ (5- y/7)dy

a.

b.

c.

d.

Step-by-step explanation:

P.S - The exact question is -

a.

y = 3x

Shape of the given integral = A Triangle

Area of Triangle = = ×1×3 =

The graph of integral is as follows :

b.

x =

⇒x² = 15 - y²

⇒x² + y² = 15

⇒x² + y² = (√15)²

Shape of the integral = Quarter circle of radius √15

Area of Quarter circle = = ××r² = ××(√15)² =

The graph of the following integral is as follows :

c.

y =

⇒y² = 81 - x²

⇒y² + x² = 81

⇒y² + x² = 9²

Shape of the integral = Semi circle of radius 9

Area of semi circle = = ××r² =  ××9² =

The graph of the following integral is as follows :

d.

x = 5 -

⇒ = 5 - x

⇒y = 35 - 7x

At y = 0 , x = 5

At y = 7 , x = 4

Shape of the integral = A triangle

Area of Triangle = ×(5-4)×7 =  ×(1)×7 =

The graph of the integral is as follows :

since proposition states that a number is greater than 25, if is true then the number must actually be greater than 25.

this implies that all possible options, except 24, can be accepted

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: