MAT136

MAT136
∫udv=uv-∫vdu - ANS-integration by parts

- ANS-Average Value of Integral

ln|x| - ANS-Integral of 1/x

(2MID(n)+TRAP(n))/3 - ANS-simp(n)

left(n)+right(n)/2 - ANS-trap(n)

f(-x) = - f(x) , symmetric with origin - ANS-odd function

f(-x) = f(x) , symmetric with y-axis - ANS-even function

∆t(f(b)-f(a)) - ANS-error Riemann sum

(b-a)/n - ANS-∆t

1/2 - ANS-Doubling n decreases the different between LEFT(n) - RIGHT(n) by exactly

trapezoid underestimates, midpoint overestimates - ANS-concave down

trapezoid overestimates, midpoint underestimates - ANS-concave up

-cosx+c - ANS-integral of sinx

sinx+c - ANS-integral of cosx

apply chain rule properly. take the derivative of the x in H(x) and derivative of the integral.
Remember the derivative of a constant is 0. helps to define function first - ANS-tip when taking
derivative of integral

don't forget c - ANS-when calculating indefinite integral

If ∫g(x) is convergent and g(x)≥f(x) for all x, then ∫f(x) is also convergent.
If ∫g(x) is divergent and g(x)≤f(x) for all x, then ∫f(x) is also divergent. - ANS-comparison test

factor out x. then apply ratio test - ANS-convergence test

1/√(1-x²) - ANS-d/dx sin⁻¹x