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MAT110U

MATHEMATICS II

2. Ünite
Soru 1
What is the area between function f(x)=x2, the lines y=9, x=0, x=3 and y-axis?
Soru 2
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?

Soru 3
I. The definite integral of a function is a real number.

II. The numbers a and b are called the lower and upper limits of the integral.

III. The variable the integral is calculated, dx, is called the integrand

What can be said to be true about definite integrals?

Soru 4
What can be said to be true about the properties of the definite integrals?
Soru 5
I. The antiderivative F of the function f will be found, i.e. ∫ f(x)dx = F(x), then, to evaluate the definite integral, the difference F(b)–F(a) will be calculated.

II. The antiderivative F of the function f will be found, i.e. ∫ f(x)dx = F(x), then, to evaluate the definite integral, the difference F(b)+F(a) will be calculated.

III. Let f be a continuous function defined on the interval [a,b] and let there be an antiderivative function F defined on the interval [a,b] such that F ' (x)=f (x). 

What can be said to be true about the fundamental theorem of calculus?

Soru 6
Soru 7
What is the value of the integral ∫f(x)= ∫(x2 + 2)2 - 4x + 5 on the interval [-1,1]?
Soru 8
Soru 9
Soru 10
Soru 11
What is the area of the plane of the region bounded by the graphs f(x)= x and g(x)=x2 + 4 on the interval [0,2]?
Soru 12
Soru 13
What is the average value of the function f(x) = x2 + 2x + 4 on the interval [0,1] ?
Soru 14
What is the value of the integral ∫f(x) = ∫ x2 + 2x + 4 on the interval [0,1] ?
Soru 15
What is the sum of squares of the natural numbers from 1 to 5?
Soru 16
What is the average value of the function f(x) = 6x2 + 2x  on the interval [1,3] ?
Soru 17
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Soru 19
Soru 20