II BOB. Integral va uning tatbiqlari — 37-39. Boshlang'ich funksiya va aniqmas integral tushunchalari — 11-sinf Algebra test savollari

1.$F(x)=\frac{x^4}{4}$ funksiya qanday f(x) funksiyaning boshlang'ich funksiyasi?

• A)$x^3$
• B)$4x^3$
• C)$x^4$
• D)$\frac{x^3}{4}$

2.$f(x)=x^5$ funksiyaning boshlang'ich funksiyalaridan birini toping.

• A)$x^6$
• B)$\frac{x^6}{6}$
• C)$5x^4$
• D)$\frac{x^4}{4}$

3.$f(x)=\cos x$ funksiyaning boshlang'ich funksiyasini toping.

• A)$-\sin x$
• B)$\cos x$
• C)$\sin x$
• D)$-\cos x$

4.$f(x)=\frac{1}{x}$, $x>0$ funksiyaning boshlang'ich funksiyasini toping.

• A)$\frac{1}{x^2}$
• B)$-\frac{1}{x^2}$
• C)$x\ln x$
• D)$\ln x$

5.a — berilgan biror son, $v(t)=at$ tezlik funksiyasi berilgan. Nuqtaning bosib o'tgan yo'li s(t) (boshlang'ich funksiyasi) ni toping.

• A)$\frac{1}{2}a{t}^2$
• B)$a{t}^2$
• C)$\frac{1}{2}{a}^{2}t$
• D)$2at$

6.$f(x)=\frac{1}{{\cos }^{2}x}$ funksiyaning boshlang'ich funksiyasini toping.

• A)$-\text{ctg}x$
• B)$\text{tg}x$
• C)$\sin x$
• D)$\frac{1}{{\sin }^{2}x}$

7.$F_1(x)=\frac{x^4}{4}$ va $F_2(x)=\frac{x^4}{4}+17$ funksiyalar qaysi f(x) funksiyaning boshlang'ich funksiyalari?

• A)$x^3+17$
• B)$4x^3$
• C)$x^3$
• D)$x^4$

8.$f(x)=x^2$ funksiyaning grafigi $A(3;10)$ nuqtadan o'tuvchi boshlang'ich funksiyasini toping.

• A)$\frac{x^3}{3}+10$
• B)$\frac{x^3}{3}-1$
• C)$x^3+1$
• D)$\frac{x^3}{3}+1$

9.$f(x)=\sqrt[3]{x}$ funksiyaning grafigi $A(8;15)$ nuqtadan o'tuvchi boshlang'ich funksiyasini toping.

• A)$\frac{3}{4}x\sqrt[3]{x}+3$
• B)$\frac{3}{4}x\sqrt[3]{x}+15$
• C)$\frac{4}{3}x\sqrt[3]{x}+3$
• D)$\frac{3}{4}x\sqrt[3]{x}-3$

10.$x<0$ bo'lganda $\int \frac{dx}{x}$ ning natijasini toping.

• A)$\ln x+C$
• B)$\ln (-x)+C$
• C)$-\ln x+C$
• D)$-\frac{1}{x}+C$