Page Description Equation
314 antiderivative \[ \]
314 indefinite integral \[ \]
314 integrand \[ \]
314 variable of integration \[ \]
314 constant of integration \[ \]
315 integral formulas table 4.1. \[ \]
316 initial value problems \[ \]
317 solve differential equations \[ \]
316 general solution \[ \]
317 particular solution \[ \]
317 mathematical modeling \[ \]
323 arithmetic rules for integration table 4.2. \[ \]
324 integrals for $\sin^2 x$ and $\cos^2 x.$ \[ \]
326 substitution method of integration (reverse chain rule) \[ \]
329 estimating integrals with finite sums \[ \]
333 displacement \[ \]
333 distance traveled (trip distance) \[ \]
333 error magnitude \[ \]
330 estimating area \[ \]
331 estimating distance \[ \]
334 estimating volume of a sphere \[ \]
335 estimating average value of a nonnegative function \[ \]
335 estimating average value of a function \[ \]
340 sigma notation \[ \]
343 partition of an interval \[ \]
343 Riemann sum for $f$ on interval $I$ \[ \]
343 limits of integration \[ \]
343 integrable function \[ \]
343 definite integral \[ \]
343 Theorem 1 Existence of Definite Integral \[ \]
344 notation for definite integrals \[ \lim\limits_{n\rightarrow\infty}\sum_{k=1}^{n} f\left(c_k\right)\Delta x =\int_a^bf\left(x\right)\dx \]
345 area under a curve \[ \]
346 average (mean) value of a function \[ \]
347 rules for definite integrals Table 4.5. \[ \]
352 Mean Value Theorem for definite integrals \[ \]
354 Theorem 3 Part I. Fundamental Theorem of Calculus \[ \]
358 Theorem 3 Part II. Fundamental Theorem of Calculus. Integral Evaluation Theorem. \[ \]
359 integral evaluation notation \[ \]
359 net area, total area \[ \]
360 how to find total area \[ \]
360 household electricity \[ \]
360 rms (root mean square) \[ \]
360 peak voltage \[ \]
360 moving coil galvanometer \[ \]
360 marginal cost, marginal revenue \[ \]
365 Substitution Formula for Definite Integrals \[ \]
365 evaluating definite integrals using antiderivatives \[ \]
367 standard normal distribution, error function \[ \]
368 area between curves \[ \]
368 how to find area between curves \[ \]
369 boundaries with changing formulas \[ \]
373 numerical integration / approximation \[ \]
373 step size \[ \]
374 Trapezoidal Rule \[ \]
376 Error Estimate for Trapezoidal Rule \[ \]
378 Simpson’s Rule \[ \]
378 Error Estimate for Simpson’s Rule \[ \]
383 the sine-integral function, continuous extension of $(\sin t )/ t.$ \[ \mathrm{Si}\left(x\right) =\int_0^xf\left(t\right)\dt\\ \text{where}\\ f\left(t\right) = \left\{ \begin{matrix} \frac{\sin t}{t}&t\neq0\\ 1&t=0\\ \end{matrix} \right. \]
383 the error function \[ \mathrm{erf}\left(x\right)=\frac{2}{\sqrt\pi}\int_{0}^{x}{e^{-t^2}dt} \]