Ünite Sınavı Soruları

What is the area of the region bounded by the curve

and the axes?

What is the area under the graph of 

on the interval

Which of the following is the mean value of the function

between

Evaluate the integral

What is the average value of the function f(x) = 6x² + 2x  on the interval [1,3] ?

I. The calculation of areas of planar regions bounded by given curves was achieved through a method called the method of exhaustion by inscribing and circumscribing the region in question by polygons the areas of which were either known or were easy to calculate.

II. Archimedes (B.C. 287-212) used this method to calculate the area of a circle (disk) by inscribing and circumscribing the circle with polygons. 

III. The area of a bounded region determined by the graph of the function y=f (x). We assume that the function f (x) is defined and continuous on a closed interval [a,b], and it is also negative, i.e. f (x) ≤ 0. 

What can be said to be true about area problems?

evaluate the upper Riemann sum for the partition

What is the area between the x-axis and the graph of the function

over the interval [-2, 1]?

Let

Calculate the lower sum of f for the partition

of the interval

What is the area between the

-axis and the graph of the function

over the interval

What is the value of the integral ∫f(x) = ∫ x² + 2x + 4 on the interval [0,1] ?

What is the area bounded by the graphs of the functions

on the interval

Evaluate the integral

For a continuous function 

then which of the following is the value of the integral 

What is the average value of the function f(x) = x² + 2x + 4 on the interval [0,1] ?