MASH Bath: Question Bank

Calculating the integral of a function of the form $\ln(ax)$ using integration by parts.

Calculating the integral of a function of the form $ax^2 e^{bx}$ using integration by parts.

Calculating the integral of a function of the form $ax^2 \cos(bx)$ using integration by parts.

Calculating the integral of a function of the form $x^n \ln(ax)$ using integration by parts.

Calculating the integral of a function of the form $(a+bx)\cos(x)$ using integration by parts.

Calculating the integral of a function of the form $ax e^{bx}$ using integration by parts.

Calculating the integral of a function of the form $ax \cos(bx)$ using integration by parts.

Calculating the integral of a function of the form $ax \sin(bx)$ using integration by parts.

Calculating the area enclosed between a cosine function and a quadratic function by integration. The limits (points of intersection) are given in the question.

Calculating the definite integral $\int_{n_1}^{n_2}a \sin(bx) dx$, where $n_1$ and $n_2$ are multiples of $\frac{\pi}{12}$.

Calculating the definite integral $\int_{n_1}^{n_2}a \sin(bx) dx$, where $n_1$ and $n_2$ are multiples of $\frac{\pi}{12}$.

Calculating the definite integral $\int_{n_1}^{n_2}a_1x^{b_1}+a_2x^{b_2}+a_3x^{b_3} dx$.

Find the derivative of a function of the form $y=a \tan(bx+c)$ using a table of derivatives.

Find the derivative of a function of the form $y=a \cos(bx+c)$ using a table of derivatives.

Calculating the derivative of an exponential function of the form $ae^{bx}$, using a table of derivatives.

Calculating the derivative of a function of the form $a \ln(bx)$ using a table of derivatives.

Find the derivative of a function of the form $y=a_1x^{b_1}+a_2x^{b_2}+a_3x^{b_3}$ using a table of derivatives.

Calculating the derivative of a function of the form $\frac{(x^2-a)^n}{x^2+a}$ using the quotient rule.

Calculating the derivative of a function of the form $\frac{ax^n+bx}{ax^n-bx}$ using the quotient rule.

Calculating the derivative of a function of the form $\frac{\ln(x)}{ax^n}$ using the quotient rule.

Calculating the derivative of a function of the form $\frac{e^{kx}}{ax^2+bx+c}$ using the quotient rule.

Calculating the derivative of a function of the form $\frac{a\sin(x)}{bx+c \cos(x)}$ using the quotient rule.

Calculating the derivative of a function of the form $\frac{ax^n+bx^m}{cx^p+d}$ using the quotient rule.

Calculating the derivative of a function of the form $\frac{ax^n}{bx+c}$ using the quotient rule.

Calculating the derivative of a function of the form $(ax+b)^n(cx+d)^m$ using the product rule.

Calculating the derivative of a function of the form $ax^n(bx^m+c)^p$ using the product rule.

Calculating the derivative of a function of the form $e^{ax} \ln(bx)$ using the product rule.

Calculating the derivative of a function of the form $\ln(ax) \tan(bx)$ using the product rule.

Calculating the derivative of a function of the form $\ln(ax) \cos(bx)$ using the product rule.

Calculating the derivative of a function of the form $\ln(ax) \sin(bx)$ using the product rule.