Applications of definite integral

2010011407

Level:

Find the area of the region bounded by the curves

y = x + 1

and

y = - x^{2} + 3

\frac{9}{2}

2

6

\frac{21}{2}

2010011406

Level:

Find the area of the region bounded by the graph of

f (x) = \sin x - 1

[\frac{π}{2}; π]

and lines

y = 0

and

x = π

\frac{π}{2} - 1

\frac{π}{2}

1

\frac{3 π}{2} - 1

2010011405

Level:

Find the area of the region bounded by

x

-axis, graph of

f (x) = x^{2} + 5

and lines

x = - 1

and

x = 2

18

24

13

\frac{52}{3}

2010011404

Level:

Find the area of the triangle

A B C

highlighted in yellow (see the picture).

16

12

8

20

2010011403

Level:

Find the area of the yellow region indicated in the picture.

2 \sqrt{2}

2 \sqrt{3}

\sqrt{2}

4 \sqrt{2}

2010011402

Level:

Find the area of the yellow triangle

A B C

indicated in the picture. Read all the needed values from the picture.

10.5

36.75

10

15.75

2010011401

Level:

Calculate the area of a plane region bounded by the graphs of the functions

f (x) = x^{2} - 2 x + 2

and

g (x) = 14 - x^{2}

\frac{125}{3}

\frac{19}{3}

\frac{93}{3}

75

Area Under the Curve II

Submitted by ladislav.foltyn on Fri, 05/31/2019 - 15:21

1003108908

Level:

What is the radius of a circle inscribed in a square, if the area of the square is given by the expression

\int_{1}^{6} (6 - x) d x

\frac{5 \sqrt{2}}{4}

3 \sqrt{2}

2 \sqrt{2}

\frac{7 \sqrt{2}}{2}

1003108907

Level:

What are the lengths of a right triangle legs, if the triangle area is given by the expression

\int_{- 4}^{1} (0.8 x + 4.2) d x - 5

5

and

4

6

and

3

4

and

6

6

and

5

Applications of definite integral

2010011407

2010011406

2010011405

2010011404

2010011403

2010011402

2010011401

Area Under the Curve II

1003108908

1003108907

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