12. Sınıf Belirsiz İntegral Ödev Hazırla

12. Sınıf – Belirsiz İntegral

Adı Soyadı:

Sınıfı:

No:

Tarih / Puan:

1) Aşağıdaki belirsiz integrali bulunuz:
\(\int -\cos(4x-1)\,dx\)

A) \(-\frac{1}{4}\cos(4x-1) + C\) B) \(-\frac{1}{4}\sin(4x-1) + C\) C) \(-1\sin(4x-1) + C\) D) \(-(-\frac{1}{4}\sin(4x-1)) + C\) E) \(\frac{1}{4}\sin(4x-1) + C\)

2) Aşağıdaki belirsiz integrali bulunuz:
\(\int 1\,dx\)

A) \(0\) B) \(-(x+3) + C\) C) \((x+3)^{0} + C\) D) \((x+3) + 3 + C\) E) \((x+3) + C\)

3) Aşağıdaki belirsiz integrali bulunuz:
\(\int -3^{3x-1}\,dx\)

A) \(\frac{-1}{3\ln 3}3^{x} + C\) B) \(\frac{-1}{\ln 3}3^{3x-1} + C\) C) \(-(\frac{-1}{3\ln 3}3^{3x-1}) + C\) D) \(\frac{-1}{3\ln 3}3^{3x-1} + C\) E) \(-\frac{1}{3}3^{3x-1} + C\)

4) Aşağıdaki belirsiz integrali bulunuz (parçalı rasyonel):
\(\int \frac{-3x-9}{\left(x+1\right)\left(x+4\right)}\,dx\)

A) \(-2\ln|x+1| - \ln|x+4| + C\) B) \(\ln\left|\frac{x+1}{x+4}\right| + C\) C) \(-2\ln|x+4| + -1\ln|x+1| + C\) D) \(-3\ln|(x+1)(x+4)| + C\) E) \(-(-2\ln|x+1| - \ln|x+4|) + C\)

5) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{1}{\sqrt{x^2-4^2}}\,dx\)

A) \(\ln\left|x+\sqrt{x^2-4^2}\right| + C\) B) \(\arccos\left(\frac{x}{4}\right) + C\) C) \(\ln|x| + C\) D) \(\sqrt{x^2-4^2} + C\) E) \(\ln\left|x+\sqrt{x^2+4^2}\right| + C\)

6) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{-2}{x}\,dx\)

A) \(-(-2\ln|x|) + C\) B) \(-2\ln|x| + C\) C) \(-2x + C\) D) \(\ln x + C\) E) \(\frac{-2}{x} + C\)

7) Aşağıdaki belirsiz integrali bulunuz:
\(\int -65^{-3x+1}\,dx\)

A) \(\frac{2}{\ln 5}5^{x} + C\) B) \(\frac{2}{\ln 5}5^{-3x+1} + C\) C) \(\frac{-6}{\ln 5}5^{-3x+1} + C\) D) \(-(\frac{2}{\ln 5}5^{-3x+1}) + C\) E) \(25^{-3x+1} + C\)

8) Aşağıdaki belirsiz integrali bulunuz (parçalı rasyonel):
\(\int \frac{-2x-4}{\left(x+1\right)\left(x-1\right)}\,dx\)

A) \(1\ln|x-1| + -3\ln|x+1| + C\) B) \(\ln|x+1| - 3\ln|x-1| + C\) C) \(-(\ln|x+1| - 3\ln|x-1|) + C\) D) \(-2\ln|(x+1)(x-1)| + C\) E) \(\ln\left|\frac{x+1}{x-1}\right| + C\)

9) Aşağıdaki belirsiz integrali bulunuz:
\(\int -4\sec^2(x-2)\,dx\)

A) \(-4\cot(x-2) + C\) B) \(-4\sec(x-2) + C\) C) \(-(-4\tan(x-2)) + C\) D) \(-4\tan(x) + C\) E) \(-4\tan(x-2) + C\)

10) Aşağıdaki belirsiz integrali bulunuz (trig dönüşüm):
\(\int \sqrt{9^2-x^2}\,dx\)

A) \(x\sqrt{9^2-x^2} + 9^2\arcsin\left(\frac{x}{9}\right) + C\) B) \(\frac{x}{2}\sqrt{9^2-x^2} + \frac{9}{2}\arcsin\left(\frac{x}{9}\right) + C\) C) \(\frac{x}{2}\sqrt{9^2-x^2} + \frac{9^2}{2}\arcsin\left(\frac{x}{9}\right) + C\) D) \(\frac{x}{2}\sqrt{9^2-x^2} - \frac{9^2}{2}\arcsin\left(\frac{x}{9}\right) + C\) E) \(\sqrt{9^2-x^2} + C\)

11) Aşağıdaki belirsiz integrali bulunuz (parçalı rasyonel):
\(\int \frac{2x-18}{\left(x-3\right)\left(x+3\right)}\,dx\)

A) \(-(-2\ln|x-3| + 4\ln|x+3|) + C\) B) \(-2\ln|x-3| + 4\ln|x+3| + C\) C) \(2\ln|(x-3)(x+3)| + C\) D) \(-2\ln|x+3| + 4\ln|x-3| + C\) E) \(\ln\left|\frac{x-3}{x+3}\right| + C\)

12) Aşağıdaki belirsiz integrali bulunuz:
\(\int -(4x+3)\,dx\)

A) \(\frac{1}{8}(4x+3)^{2} + C\) B) \(-\frac{1}{4}(4x+3)^{2} + C\) C) \(-\frac{1}{8}(4x+3)^{2} + C\) D) \(-\frac{1}{8}(4x+3) + C\) E) \(-\frac{1}{2}(4x+3)^{2} + C\)

13) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{-1}{-2x}\,dx\)

A) \(\frac{1}{2}-2x + C\) B) \(\frac{1}{2}\ln|-2x| + C\) C) \(-1\ln|-2x| + C\) D) \(-(\frac{1}{2}\ln|-2x|) + C\) E) \(\ln|-2x| + C\)

14) Aşağıdaki belirsiz integrali bulunuz:
\(\int \sin(3x-4)\,dx\)

A) \(-\frac{1}{3}\cos(3x-4) + C\) B) \(-(-\frac{1}{3}\cos(3x-4)) + C\) C) \(\frac{1}{3}\cos(3x-4) + C\) D) \(1\cos(3x-4) + C\) E) \(-\frac{1}{3}\sin(3x-4) + C\)

15) Aşağıdaki belirsiz integrali bulunuz (trig dönüşüm):
\(\int \sqrt{2^2-x^2}\,dx\)

A) \(x\sqrt{2^2-x^2} + 2^2\arcsin\left(\frac{x}{2}\right) + C\) B) \(\frac{x}{2}\sqrt{2^2-x^2} + \frac{2}{2}\arcsin\left(\frac{x}{2}\right) + C\) C) \(\frac{x}{2}\sqrt{2^2-x^2} - \frac{2^2}{2}\arcsin\left(\frac{x}{2}\right) + C\) D) \(\sqrt{2^2-x^2} + C\) E) \(\frac{x}{2}\sqrt{2^2-x^2} + \frac{2^2}{2}\arcsin\left(\frac{x}{2}\right) + C\)

16) Aşağıdaki belirsiz integrali bulunuz:
\(\int 3\sec^2(-4x+2)\,dx\)

A) \(-\frac{3}{4}\cot(-4x+2) + C\) B) \(-\frac{3}{4}\tan(-4x+2) + C\) C) \(-\frac{3}{4}\sec(-4x+2) + C\) D) \(-(-\frac{3}{4}\tan(-4x+2)) + C\) E) \(3\tan(-4x+2) + C\)

17) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{-3}{\sqrt{1-x^2}}\,dx\)

A) \(-3\sin x + C\) B) \(-3\ln|1-x^2| + C\) C) \(-(-3\arcsin x) + C\) D) \(-3\arcsin x + C\) E) \(\arctan x + C\)

18) Aşağıdaki belirsiz integrali bulunuz:
\(\int x^{2}\,dx\)

A) \(\frac{1}{3}x^{3} + C\) B) \(\frac{1}{3}x^{4} + C\) C) \(\frac{1}{3}x^{2} + C\) D) \(-\frac{1}{3}x^{3} + C\) E) \(x^{3} + C\)

19) Aşağıdaki belirsiz integrali bulunuz:
\(\int -4e^{-3x}\,dx\)

A) \(-4e^{-3x} + C\) B) \(\frac{4}{3}(-3x)e^{-3x} + C\) C) \(-(\frac{4}{3}e^{-3x}) + C\) D) \(\frac{4}{3}e^{x} + C\) E) \(\frac{4}{3}e^{-3x} + C\)

20) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{-4}{\sqrt{1-x^2}}\,dx\)

A) \(-4\ln|1-x^2| + C\) B) \(-4\arcsin x + C\) C) \(-4\sin x + C\) D) \(\arctan x + C\) E) \(-(-4\arcsin x) + C\)