Miscellaneous Exercises (VCE SSCE Mathematical Methods): Quizzes

📚Quizzes
Miscellaneous exercises
Sign up to keep practising.Create a free account to play more quizzes and track your progress.

Practise the questions

10 questions from this quiz

Show

What key technique helps evaluate integrals by recognizing patterns?

Working backwards from derivative patterns

If f(x)=loge(x2+1)f(x) = \log_e(x^2 + 1), what is f(x)f'(x)?

2xx2+1\frac{2x}{x^2 + 1}

What is 02xx2+1dx\int_0^2 \frac{x}{x^2 + 1} dx?

12loge5\frac{1}{2} \log_e 5

If f(x)=cosxsinxf(x) = \frac{\cos x}{\sin x}, what is f(x)f'(x)?

1sin2x\frac{-1}{\sin^2 x}

What is π4π21sin2xdx\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{1}{\sin^2 x} dx?

11

What is loge(kx)dx\int \log_e(kx) dx where kk is a positive constant?

xloge(kx)x+cx \log_e(kx) - x + c

What is xloge(kx)dx\int x \log_e(kx) dx where kk is a positive constant?

12x2loge(kx)x24+c\frac{1}{2}x^2 \log_e(kx) - \frac{x^2}{4} + c

If f(x)=xloge(kx)f(x) = x \log_e(kx), what is f(x)f'(x)?

loge(kx)+1\log_e(kx) + 1

When should you use CAS calculators for integration?

Complex expressions beyond current techniques

Which function has no simple antiderivative in elementary functions?

ex2e^{-x^2}

Join 100,000+ SSCE students studying Quizzes with us.

Select your subjects, and get access to A+ resources today.