Expand knowledge base

1 files changed, 4 insertions, 4 deletions

diff --git a/content/know/concept/calculus-of-variations/index.pdc b/content/know/concept/calculus-of-variations/index.pdc
index 26c5753..9cae283 100644
--- a/content/know/concept/calculus-of-variations/index.pdc
+++ b/content/know/concept/calculus-of-variations/index.pdc
@@ -251,7 +251,7 @@ meaning they do not depend on any derivatives of any $f_n(x)$:
 
 $$\begin{aligned}
     \phi_m(f_1, ..., f_N, x) = 0
-    \qquad
+    \qquad \qquad
     \int_{x_0}^{x_1} \phi_m(f_1, ..., f_N, x) \dd{x} = C_m
 \end{aligned}$$
 
@@ -261,12 +261,12 @@ by simply redefining the constraint as $\phi_m^0 = \phi_m - C_m = 0$.
 
 To solve this constrained optimization problem for $f_n(x)$,
 we introduce [Lagrange multipliers](/know/concept/lagrange-multiplier/) $\lambda_m$.
-In the former case $\lambda_m(x)$ is a function of all $x$, while in the
+In the former case $\lambda_m(x)$ is a function of $x$, while in the
 latter case $\lambda_m$ is constant:
 
 $$\begin{aligned}
-    \int \lambda_m(x_i) \: \phi_m(\{f_n\}, x) \dd{x} = 0
-    \qquad
+    \int \lambda_m(x) \: \phi_m(\{f_n\}, x) \dd{x} = 0
+    \qquad \qquad
     \lambda_m \int \phi_m(\{f_n\}, x) \dd{x} = \lambda_m C_m
 \end{aligned}$$