Question

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Find the area under the graph of f over the interval left bracket 7 comma 9...

Find the area under the graph of f over the interval

left bracket 7 comma 9 right bracket[7,9].

f(x)equals=StartSet Start 2 By 2 Matrix 1st Row 1st Column 4 x plus 9 comma 2nd Column for x less than or equals 8 2nd Row 1st Column 81 minus 5 x comma 2nd Column for x greater than 8 EndMatrix

4x+9,	for x≤8
81−5x,	for x>8

The area is

nothing.

Find the area of the region bounded by the graphs of the given equations.

yequals=x plus 6x+6,

yequals=x squaredx2

The area is

nothing.

(Type an integer or a simplified fraction.)

Solutions

Expert Solution

1) The two lines intersect when

4x+9 = 81−5x

9x = 72, i.e. x = 8

Since they intersect in the middle of given interval [7, 9] hence from 7 ≤ x ≤ 8 one line will be over the other, and in the other interval 8 ≤ x ≤ 9 it will be the other way round. This can also be shown in the sketch below.

Hence, the required area is

2) The two curves intersect when

Hence, we need to find area in the interval -2 ≤ x ≤ 3. In this intevral, the line is above the parabola. This can be sketvhed as below

Hence, the required area is

milcah answered 1 year ago

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