Fix typos in the document

book/labs/1_Color_Labs/2_Human_Perception/lab03.ipynb

@@ -196,8 +196,8 @@
     "\\begin{align*}\n",
     "    R_S &= \\int_{390}^{700} [a S_1(\\lambda) + b S_2(\\lambda)] Q_R(\\lambda)d\\lambda \\\\ \n",
     "    &= \\int_{390}^{700} [a S_1(\\lambda)Q_R(\\lambda) + b S_2(\\lambda)Q_R(\\lambda)] d\\lambda \\\\ \n",
-    "    &= \\int_{390}^{700} a S_1(\\lambda)d\\lambda  + \\int_{390}^{700} b S_2(\\lambda) Q_R(\\lambda)d\\lambda \\\\ \n",
-    "    &= a \\int_{390}^{700} S_1(\\lambda)d\\lambda  + b \\int_{390}^{700} S_2(\\lambda) Q_R(\\lambda)d\\lambda \\\\ \n",
+    "    &= \\int_{390}^{700} a S_1(\\lambda) Q_R(\\lambda)d\\lambda  + \\int_{390}^{700} b S_2(\\lambda) Q_R(\\lambda)d\\lambda \\\\ \n",
+    "    &= a \\int_{390}^{700} S_1(\\lambda) Q_R(\\lambda)d\\lambda  + b \\int_{390}^{700} S_2(\\lambda) Q_R(\\lambda)d\\lambda \\\\ \n",
     "    &= a R_1 + b R_2.\n",
     "\\end{align*}"
    ]
@@ -210,13 +210,14 @@
     "\n",
     "Calculate the tristimulus vector with respect to the stimulus $\n",
     "    S(\\lambda) = \\begin{cases}\n",
-    "        1, 450 \\leq \\lambda \\leq 650 \\\\ \n",
-    "        0, \\text{ otherwise} \n",
+    "        1,   450 \\leq \\lambda \\leq 650 \\\\ \n",
+    "        0,   \\text{ otherwise} \n",
     "    \\end{cases}$\n",
     "in two ways:\n",
     "1. Using the trapezoidal rule to estimate $R_S,G_S,B_S$\n",
     "2. Using your polynomial interpolants of $Q_R,Q_G,$ and $Q_B$ to integrate symbolically\n",
     "\n",
+    "The bounds of the integral and trapezoidal sum will be 450 to 650 because that is where S(\\lambda) is 1.\n",
     "For the symbolic integration, see the example below using `Polynomial.integ`.\n",
     "\n",
     "<h3 style=\"background-color:lightblue\"> Write Answers for Exercise 4 Below </h3>"
@@ -246,7 +247,7 @@
     "The spectrum of the CIE D65 illuminant can be downloaded from [here](https://github.com/TheDataScienceLabs/DataLab_Multivariate_Calculus/blob/main/book/labs/1_Color_Labs/2_Human_Perception/d65_spectrum.txt).\n",
     "\n",
     "Calculate the tristimulus vector where the stimulus $S(\\lambda)$ is the D65 illuminant in two ways:\n",
-    "1. Using the trapezoidal rule to estimate the three integrals\n",
+    "1. Using the trapezoidal rule to estimate the three integrals (bounds are 390 to 700 because S(\\lambda) has non zero values in this range)\n",
     "1. Approximating the spectral power distribution of the illuminant with a high enough degree polynomial and using your polynomial interpolants of $Q_R,Q_G,$ and $Q_B$ to integrate symbolically. Justify your choice of a \"high enough degree polynomial\" for the D65 illuminant.\n",
     "\n",
     "<h3 style=\"background-color:lightblue\"> Write Answers for Exercise 5 Below </h3>"