Overview (Leaving Cert Applied Maths): Quizzes

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What is the integral of xnx^n using the power rule?

xn+1n+1+c\frac{x^{n+1}}{n+1} + c

Why must we include a constant cc when integrating?

Differentiation of a constant gives zero

What is the integral of 1ax+b\frac{1}{ax + b}?

1aln⁡(ax+b)+c\frac{1}{a}\ln(ax + b) + c

The fundamental theorem states ∫abf(x)dx\int_a^b f(x)dx equals what?

F(b)−F(a)F(b) - F(a)

In INLATE, which function type should be chosen first for uu in integration by parts?

Inverse trigonometric

How is velocity vv related to distance ss with respect to time?

v=dsdtv = \frac{ds}{dt}

Acceleration is which derivative of distance?

Second derivative

What formula calculates work done by a variable force from position aa to bb?

W=∫abF(x)dxW = \int_a^b F(x)dx

What distinguishes a particular solution from a general solution?

Uses initial conditions for constant

What does separating variables in differential equations involve?

Collecting each variable on different sides

For second-order DEs, letting v=dydxv = \frac{dy}{dx} transforms d2ydx2\frac{d^2y}{dx^2} into what?

vdvdyv\frac{dv}{dy}

If PP is proportional to QQ, what is the relationship?

P=kQP = kQ

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