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Prueba de Integrales Trigonométricas

Authored by Santiago Torres

Mathematics

12th Grade

Used 3+ times

Prueba de Integrales Trigonométricas
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12 questions

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1.

MULTIPLE CHOICE QUESTION

3 mins • 5 pts

Calcular la integral de cos(x) * ln(x) dx utilizando integración por partes.

ln(x) * sin(x) + C

cos(x) * sin(x) + C

ln(x) * cos(x) + C

cos(x) * x * ln(x) + C

2.

MULTIPLE CHOICE QUESTION

3 mins • 5 pts

(9/2) * (sin^(-1)(x/3) + x * sqrt(9 - x^2)/9) + C

(9/2) * (cot^(-1)(x/3) + x * sqrt(9 - x^2)/9) + C

(9/2) * (tan^(-1)(x/3) + x * sqrt(9 - x^2)/9) + C

(9/2) * (cos^(-1)(x/3) + x * sqrt(9 - x^2)/9) + C

3.

MULTIPLE CHOICE QUESTION

3 mins • 5 pts

Hallar la integral de tan(x) sec^2(x) dx.

sin(x) + C

cos(x) + C

ln|sec(x)| + C

ln|tan(x)| + C

4.

MULTIPLE CHOICE QUESTION

3 mins • 5 pts

Calcular la integral de sin^3(x) cos(x) dx utilizando identidades trigonométricas.

sin^3(x) + cos(x) + C

(1/4) * sin^2(x) * cos(x) + (1/2) * cos^2(x) + C

sin(x) * cos^3(x) + C

sin^2(x) * cos(x) + cos^2(x) + C

5.

MULTIPLE CHOICE QUESTION

3 mins • 5 pts

Resolver la integral de 1 / (x^2 + 1) dx mediante integración por sustitución.

1/2 ln|x^2 - 1| + C

1/2 ln|x^2 + 1| + C

1/2 ln|x^2| + C

ln|x^2 + 1| + C

6.

MULTIPLE CHOICE QUESTION

3 mins • 5 pts

Hallar la integral de sec(x) tan(x) dx.

sec(x) + ln|sec(x) + tan(x)| + C

sec(x) - ln|sec(x) - tan(x)| + C

sec(x) + ln|sec(x) - tan(x)| + C

sec(x) - ln|sec(x) + tan(x)| + C

7.

MULTIPLE CHOICE QUESTION

3 mins • 5 pts

Calcular la integral de x / sqrt(1 - x^2) dx mediante sustitución trigonométrica.

cos^(-1)(x) + C

tan^(-1)(x) + C

sec^(-1)(x) + C

sin^(-1)(x) + C

Answer explanation

La integral de x / sqrt(1 - x^2) dx mediante sustitución trigonométrica es sin^(-1)(x) + C.

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