∫ ( f(x) * g'(x) ) dx = f(x) * g(x) - ∫ ( f'(x) * g(x) ) dx

∫ ( f(x) * g'(x) ) dx = f(x) * g(x) + ∫ ( f'(x) * g(x) ) dx

∫ ( f(x) * g'(x) ) dx = f(x) * g(x) - ∫ ( f(x) * g(x) ) dx

∫ ( f(x) * g(x) ) dx = f(x) * g(x) - ∫ ( f'(x) * g(x) ) dx

ak = (π / 2) (-π)∫(π) ( f(x) * cos(k*x ) ) dx

ak = (1 / π) (-e)∫(π) ( f(x) * cos(k*x ) ) dx

ak = (1 / π) (-π)∫(π) ( f(x) * cos(k*x ) ) dx

ak = (1 / π) (-π)∫(π) ( f(x) * sin(k*x ) ) dx

bk = (1 / π) (-π)∫(π) ( f(x) * sin(e*x ) ) dx

bk = (1 / π) (-π)∫(π) ( f(x) * sin(k*x ) ) dx

bk = (π / 2) (-π)∫(π) ( f(x) * sin(k*x ) ) dx

bk = (1 / π) (-π)∫(π) ( -f(x) * -sin(k*x ) ) dx

f(x) = (a0 / 2) + (∞)∑ (k=1) ( (ak * cos(k*x) + bk *sin(k*x) )

f(x) = (a0 / 2) + (∞)∑ (k=1) ( (bk * cos(k*x) + ak *sin(k*x) )

f(x) = (a0 / 2) + (∞)∑ (k=1) ( (ak * sin(k*x) + bk *sin(k*x) )

f(x) = (a0 / 2) - (∞)∑ (k=1) ( (ak * cos(k*x) - bk *sin(k*x) )

∫ ( f(x) ) dx = (( b - a ) / n ) * f(x0) + ... + (( b - a ) / n ) * f(xn-1)

∫ ( f(x) ) dx = (( b - a ) / n ) * f(x0) + ... + (( a - b ) / n ) * f(xn-1)

∫ ( f(x) ) dx = (( b - a ) / n ) * f(x0) + ... + (( b - a ) / n ) * f(xn)

∫ ( f(x) ) dx = (( b - a ) / b ) * f(x0) + ... + (( b - a ) / n ) * f(xn-1)

∫ ( f(x) ) dx = ( b - a ) * (( f(a) + f(b) ) / 2 )

∫ ( f(x) ) dx = ( a - b ) * (( f(a) + f(b) ) / 2 )

∫ ( f(x) ) dx = ( b - a ) * (( f(a) + f(b) ) / 4 )

∫ ( f(x) ) dx = ( b - a ) * (( f(n) + f(a) ) / 2 )

∫ ( f(x) ) dx = (( b - a ) / (6*n)) * ( f(x0) + 4 * f(x1) + 2 * f(x2) + 4 * f(x3) + ... + 2 * f(x2n-2) + 4 * f(x2n-1) + f(x2n) )

∫ ( f(x) ) dx = (( a - b ) / (6*n)) * ( f(x0) + 4 * f(x1) + 2 * f(x2) + 4 * f(x3) + ... + 2 * f(x2n-2) + 4 * f(x2n-1) + f(x2n) )

∫ ( f(x) ) dx = (( b - a ) / (2*n)) * ( f(x0) + 4 * f(x1) + 2 * f(x2) + 4 * f(x3) + ... + 2 * f(x2n-2) + 4 * f(x2n-1) + f(x2n) )

∫ ( f(x) ) dx = (( b - a ) / (6*n)) * ( f(x0) + 4 * f(x1) + 2 * f(x2) + 4 * f(x3) + ... + 2 * f(xn-2) + 4 * f(xn-1) + f(xn) )

L = √( ( f(b) + f(a) )² + ( g(b) + g(a) )² )

L = √( ( f(b) - f(a) )² - ( g(b) - g(a) )² )

L = √( ( f(b) - f(b) )² + ( g(a) - g(a) )² )

L = √( ( f(b) - f(a) )² + ( g(b) - g(a) )² )

( 1 - t ) * P0 + t * P1

( 1 - t ) * P1 - t * P0

t * P0 + (1 - t ) * P1

t * P0 + t * P1

g(x) = x * (f(x)/f'(x))

g(x) = x / (f(x)/f'(x))

g(x) = x + (f(x)/f'(x))

g(x) = x * (F(x)/f'(x))