مكثف الرياضيات الفصل الثاني محمد صالح

Question One

1- $\int_{1}^{e^{2}} \frac{1}{1 - e} d x$

\frac{e^{2}}{1 - e}

- 1 - e

1 + e

- In |\begin{matrix} 1 - e^{2} \end{matrix}|

Question Two

2- $\int_{0}^{1} 3^{2 x + 1} d x$

\frac{12}{I n 3}

\frac{8}{I n 3}

12

\frac{13}{I n 3}

Question Three

3- $\int_{0}^{I n 5} e^{2 x} d x$

\frac{25}{2}

25

24

12

Question Four

4- $\int_{- π}^{\frac{π}{2}} |\sin x| d x$

- 1

1

3

2

Question Five

5- اذا كان $\int_{0}^{k} |2 x - 2| d x = 5$ $جد الثابت k$ $k > 1$

2

1

3

غير ذلك

Question Six

6- اذا كان $\int_{1}^{a} \sqrt{x d x} = 1$ $، حيث a ثابت$ جد $\int_{a}^{1} \frac{2 x}{\sqrt{x}} d x$

\frac{1}{2}

- 2

2

- 1

Question Seven

7- اذا كان $\int_{- 3}^{3} (3 x^{2} - 2 \int_{0}^{b} 3 u d u) d x = - 20$ ما قيمة الثابت b

\pm 2

2

\pm 4

- 2

Question Eight

8- $\int_{0}^{\sqrt{3}} \frac{x^{3}}{\sqrt{x^{2} + 1}} d x$

2

\frac{4}{3}

\frac{7}{3}

\frac{10}{3}

Question Nine

9- $\int_{1}^{e} 4 x^{2} e^{I n x} d x$

e^{4} - 1

e^{4} + 1

e^{3} - 1

4 (e - 1)

Question Ten

10- $\int_{\frac{π}{4}}^{\frac{π}{6}} (\frac{\sin 3 x}{\sin x} - \frac{\cos 3 x}{c o x x}) d x$

0

\frac{- 1}{4}

- \frac{π}{12}

- \frac{π}{6}

Question Eleven

11- $\int_{0}^{I n 3} \frac{e^{x}}{4 + e^{x}} d x$

I n 7

I n 5

I n \frac{7}{5}

I n \frac{5}{7}

Question Twelve

12- $\int_{0}^{\frac{π}{3}} \frac{\sin 2 x}{\cos^{3} x} d x$

2

4

\frac{1}{2}

- 1

Question Thirteen

$b$ جد قيمة الثابت $\int_{0}^{I n b} e^{2 x} d x = \frac{3}{2}$

1

\pm 2

e

2

Question Fourteen

14- $\int_{- 3}^{3} (3 - |1 - x|) d x$

7

0

8

17

Question Fifteen

15- $\int_{0}^{2} (x - 1) e^{{(x - 1)}^{2}} d x$

1

- 1

e - 1

0

Question Sixteen

16- $\int_{- 1}^{1} x^{2} {(x + 1)}^{2} d x$

\frac{32}{5}

\frac{16}{15}

- \frac{32}{5}

- \frac{16}{15}

Question Seventeen

17- اذا كان $\int_{1}^{3} v d u = 8$ وكان $u (1) = v (1) = 2$

$u (3) = 1, v (3) = 4$ فإن $\int_{3}^{1} u d v$

- 8

8

- 10

10

Question Eighteen

18- اذا كان $f (x) = \{\begin{matrix} \cos x, 0 \leq x < π \\ - 1, n \leq x \leq 2 π \end{matrix}\}$ جد $\int_{0}^{2 π} f (x) d x$

2 π

- 2 π

π

- π

Question Nineteen

19- $\int_{0}^{1} \frac{2 x - 3}{2 x^{2} - 6 x - 2} d x$

I n 3

I n \sqrt{2}

I n \sqrt{3}

I n 2

Question Twenty

20- ما قيمة $\int_{1}^{3} ه I n 8 x d x + \int_{3}^{1} I n 2 x d x$

I n 16

I n 4

I n 8

I n 2

Question Twenty-One

21- $\int {e^{x}}^{2} + I n x d x$

e^{x^{2}} + c

\frac{1}{2} e^{x^{2}} + c

e^{x^{3}} + c

\frac{1}{2} e^{x} + c

Question Twenty-Two

22- $\int_{0}^{4} \frac{x}{\sqrt{2 x + 1}} d x$

\frac{10}{3}

\frac{20}{3}

4

- 8

Question Twenty-Three

23- $\int_{1}^{3} \frac{x^{2}}{x^{3} + 3 x} d x$

I n 3

I n 6

I n 2

I n \sqrt{3}

Question Twenty-Four

24- $\int_{\frac{1}{2}}^{1} \frac{{(x - 1)}^{4}}{x^{6}} d x$

- \frac{1}{5}

\frac{1}{5}

\frac{1}{6}

\frac{1}{4}

Question Twenty-Five

25- $\int \frac{x}{x^{4} + x^{2}} d x$

\frac{1}{2} I n |1 + x^{- 2}| + c

- \frac{1}{2} I n |1 + x^{- 2}| + c

I n |1 + x^{2}| + c

I n |x^{2} + x| + c

Question Twenty-Six

26- $\int \sin x s e c^{2} x d x$

s e c x + c

t e n x + c

c s c x + c

s e c^{2} x + c

Question Twenty-Seven

27- $\int \frac{x - \sqrt{x}}{\sqrt{x - 1}} d x$

\frac{3}{2} \sqrt{x} + c

\frac{2}{3} \sqrt{x} + c

\frac{2}{3} \sqrt[3]{x} + c

\frac{2}{3} \sqrt{x^{3}} + c

Question Twenty-Eight

$\int_{a}^{b} f' (h (x)) h' (x) d x$

f (b) - f (a)

f' (b) - f' (a)

f (h (b)) - f (h (a))

f (h (a)) - f (h (b))

Question Twenty-Nine

29- $\int \frac{\tan x}{\cos x} d x$

s e c x + c

- s e c x + c

c s c x + c

- c s c x + c

Question Thirty

30- اذا كان $M = \int_{\frac{π}{4}}^{\frac{3 π}{4}} c s c^{2} x d x, k = \int_{\frac{3 π}{4}}^{\frac{π}{3}} c o t^{2} x d x$ ما قيمة $M + K$

- 1

- \frac{π}{2}

1

\frac{π}{2}

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