Question

Help with 2 calculus question?

Answer 1

The function f(x) = x² - 4x

y = x² - 4x

And the line y = x - 4

Equate the functions.

x² - 4x = x - 4

x² - 4x - x + 4 = 0

x( x - 4) - 1(x - 4) = 0

(x - 4)(x - 1) = 0

x = 4 and x = 1

The limits a = 1, b = 4

Formula for the area of the region bounded by the graphs of y = x² - 4x and the line y = x - 4

In this case f(x) = x - 4, g(x) = x² - 4x

= 4.5 square units.

Option B is correct .

Answer 2

The function y = x²

And the line x + y = 2

y = 2 - x

x axis y = 0

Substitute y = 0 in the above equations.

Substitute y = 0 in y = x².

x² = 0

x = 0

Substitute y = 0 in x + y = 2

x = 2

Formula for the area

In this case f(x) = 2 - x , g(x) = x²

The area of the region in the first quadrant bounded by the x - axis,y = x²  and x + y = 2

Second option is correct.