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FIRST QUIZ IN INTEGRAL CALCULUS

Authored by Vincent Acuña

Engineering

12th Grade

FIRST QUIZ IN INTEGRAL CALCULUS
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7 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

5 mins • 3 pts

Evaluate the ∫xcos⁡4x dx_{Evaluate\ the\ \int_{ }^{ }x\cos4x\ dx}

xcos⁡4x4+cos⁡4x16 + c\frac{x\cos4x}{4}+\frac{\cos4x}{16}\ +\ c

xsin⁡4x4 + cos⁡4x16 + c\frac{x\sin4x}{4}\ +\ \frac{\cos4x}{16}\ +\ c

xsin⁡4x4 − cos⁡4x16 + c\frac{x\sin4x}{4}\ -\ \frac{\cos4x}{16}\ +\ c

xsun4x4 + cos⁡4x16 + c\frac{xsun4x}{4}\ +\ \frac{\cos4x}{16}\ +\ c

2.

MULTIPLE CHOICE QUESTION

5 mins • 4 pts

Evaluate the ∫2x2e4x dxEvaluate\ the\ \int_{ }2x^2e^{4x}\ dx

x2e4x2 − xe4x4+e4x16 + c\frac{x^2e^{4x}}{2}\ -\ \frac{xe^{4x}}{4}+\frac{e^{4x}}{16}\ +\ c

x2e4x2 − xe4x4−e4x16 + c\frac{x^2e^{4x}}{2}\ -\ \frac{xe^{4x}}{4}-\frac{e^{4x}}{16}\ +\ c

x2e4x2 + xe4x4+e4x16 + c\frac{x^2e^{4x}}{2}\ +\ \frac{xe^{4x}}{4}+\frac{e^{4x}}{16}\ +\ c

−x2e4x2 − xe4x4+e4x16 + c-\frac{x^2e^{4x}}{2}\ -\ \frac{xe^{4x}}{4}+\frac{e^{4x}}{16}\ +\ c

3.

MULTIPLE CHOICE QUESTION

3 mins • 3 pts

The antiderivative of 4xe2x dx is 2xex−e2x + cThe\ antiderivative\ of\ 4xe^{2x}\ dx\ is\ 2xe^x-e^{2x}\ +\ c

True
False

4.

MULTIPLE CHOICE QUESTION

10 mins • 5 pts

Evaluate the ∫e2xsin⁡6x dxEvaluate\ the\ \int_{ }^{ }e^{2x}\sin6x\ dx

e2xsin⁡6x10 − 3e2xcos⁡6x20 + c\frac{e^{2x}\sin6x}{10}\ -\ \frac{3e^{2x}\cos6x}{20}\ +\ c

e2xsin⁡6x20 − 3e3xcos⁡6x20 + c\frac{e^{2x}\sin6x}{20}\ -\ \frac{3e^{3x}\cos6x}{20}\ +\ c

−e2xsin⁡6x20 − 3e2xcos⁡6x20 + c-\frac{e^{2x}\sin6x}{20}\ -\ \frac{3e^{2x}\cos6x}{20}\ +\ c

e2xsin⁡6x20 − 3e2xcos⁡6x20 + c\frac{e^{2x}\sin6x}{20}\ -\ \frac{3e^{2x}\cos6x}{20}\ +\ c

5.

MULTIPLE CHOICE QUESTION

30 sec • 2 pts

Integration by algebraic substitution is used when a certain algebraic function can't be integrated directly.

True
False

6.

FILL IN THE BLANKS QUESTION

1 min • 3 pts

*Write your answer in ALL CAPITAL LETTERS.

Integral calculus involves integrating all kinds of functions like polynomial functions, trigonometric functions, exponential functions, logarithmic functions, inverse trigonometric functions, (a)   functions and complex functions.

7.

MULTIPLE CHOICE QUESTION

15 mins • 10 pts

Evaluate the ∫3x2arccot⁡x dxEvaluate\ the\ \int_{ }^{ }3x^2\operatorname{arccot}x\ dx

x3arccot⁡x − x22−ln⁡∣1 + x2∣2+ cx^3\operatorname{arccot}x\ -\ \frac{x^2}{2}-\frac{\ln\left|1\ +\ x^2\right|}{2}+\ c

x3arccot⁡x + x22−ln⁡∣1 + x2∣2+ cx^3\operatorname{arccot}x\ +\ \frac{x^2}{2}-\frac{\ln\left|1\ +\ x^2\right|}{2}+\ c

x3arccot⁡x + x22−ln⁡∣1 − x2∣2+ cx^3\operatorname{arccot}x\ +\ \frac{x^2}{2}-\frac{\ln\left|1\ -\ x^2\right|}{2}+\ c

x3arccot⁡x − x22+ln⁡∣1 − x2∣2+ cx^3\operatorname{arccot}x\ -\ \frac{x^2}{2}+\frac{\ln\left|1\ -\ x^2\right|}{2}+\ c

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