Update ti8 check it

source/calculus/exercises/outcomes/TI/TI8/generator.sage

@@ -1,49 +1,99 @@
 class Generator(BaseGenerator):
     def data(self):
+        from sage.symbolic.integration.integral import definite_integral
+
         x=var("x")
         tasks = []
 
-        bs = sample([choice([-1,1])*n for n in range(2,10)],4)
+        bs = sample([choice([-1,1])*n for n in range(2,10)],5)
+
+        coeff = [2,3,4,5,6,7,8]
+
+        case1 = choice([0,1])
 
         # converges with infinite bound
-        p = randrange(3,10)
-        q = randrange(2,p)
-        tasks.append({
-            "integrand": 1/(x-bs[0])^(SR(p)/q),
-            "converges": True,
-            "top": oo,
-            "bottom": bs[0]+randrange(1,6),
-        })
+        if case1 == 0:
+            p = randrange(3,10)
+            q = randrange(3,10)
+            bottom = bs[0] + randrange(1,6)
+            shuffle(coeff)
+            antidiff(x) = -1*(coeff[0]/coeff[1])/(x-bs[0])^(SR(p)/q)
+            tasks.append({
+                "integrand": antidiff(x).diff(x),
+                "converges": True,
+                "top": oo,
+                "bottom": bottom,
+                "proper": False,
+                "improper": True,
+                "int": 0-antidiff(bottom),
+            })
 
         # diverges with infinite bound
-        p = randrange(2,9)
-        q = randrange(p+1,10)
-        tasks.append({
-            "integrand": 1/(x-bs[1])^(SR(p)/q),
-            "converges": False,
-            "top": oo,
-            "bottom": bs[1]+randrange(1,6),
-        })
+        if case1 == 1:
+            p = randrange(1,5)
+            q = randrange(p+1,p+5)
+            bottom = bs[1]+randrange(1,6)
+            shuffle(coeff)
+            antidiff(x) = choice([(coeff[0]/coeff[1])*(x-bs[1])^(SR(p)/q), (coeff[0]/coeff[1])*log(x-bs[1]) ])
+            tasks.append({
+                "integrand": antidiff(x).diff(x),
+                "converges": False,
+                "top": oo,
+                "bottom": bottom,
+                "proper": False,
+                "improper": True,
+                "int": r"\infty",
+            })
 
         # converges with finite bounds
-        p = randrange(2,9)
-        q = randrange(p+1,10)
-        tasks.append({
-            "integrand": 1/(x-bs[2])^(SR(p)/q),
-            "converges": True,
-            "top": bs[2]+randrange(1,6),
-            "bottom": bs[2],
-        })
+        if case1 == 1:
+            case1 = randrange(0,2)
+            p = randrange(1,5)
+            q = randrange(p+1,p+5)
+            top = bs[2]+randrange(1,6)
+            shuffle(coeff)
+            antidiff(x) = (coeff[0]/coeff[1])*(x-bs[2])^(SR(p)/q)
+            tasks.append({
+                "integrand": antidiff(x).diff(x),
+                "converges": True,
+                "top": top,
+                "bottom": bs[2],
+                "proper": False,
+                "improper": True,
+                "int": antidiff(top),
+            })
 
         # diverges with finite bounds
+        if case1 == 0:
+            p = randrange(3,10)
+            q = randrange(3,10)
+            top = bs[3]+randrange(1,6)
+            shuffle(coeff)
+            antidiff(x) = choice([-1*(coeff[0]/coeff[1])/(x-bs[3])^(SR(p)/q), (coeff[0]/coeff[1])*log(x-bs[3]) ])
+            tasks.append({
+                "integrand": 1/(x-bs[3])^(SR(p)/q),
+                "converges": False,
+                "top": top,
+                "bottom": bs[3],
+                "proper": False,
+                "improper": True,
+                "int": r"\infty",
+            })
+
+
+        # proper
         p = randrange(3,10)
-        q = randrange(2,p)
+        q = randrange(3,10)
+        bottom = bs[4]+randrange(1,6)
+        top = bottom + randrange(1,6)
         tasks.append({
-            "integrand": 1/(x-bs[3])^(SR(p)/q),
-            "converges": False,
-            "top": bs[3]+randrange(1,6),
-            "bottom": bs[3],
-        })
+            "integrand": 1/(x-bs[4])^(SR(p)/q),
+            "converges": True,
+            "top": top,
+            "bottom": bottom,
+            "proper": True,
+            "improper": False,
+        })    
 
         shuffle(tasks)
 

source/calculus/exercises/outcomes/TI/TI8/template.xml

@@ -2,20 +2,19 @@
 <knowl mode="exercise" xmlns="https://spatext.clontz.org" version="0.2">
     <intro>
         <p>
-Explain and demonstrate how to write each of the following improper integrals
-as a limit, and why this limit converges or diverges.
+For each of the following integrals, identify if the integral is proper or improper.  If improper, then compute the integral by finding the antiderivative, using the fundamental theorem of calculus, and computing the limit.
         </p>
     </intro>
     <!-- {{#tasks}} -->
     <knowl>
-        <content><p><m>\displaystyle\int_{ {{bottom}} }^{ {{top}} } {{integrand}} dx.</m></p></content>
+        <content><p><m>\renewcommand{\log}{\ln} \displaystyle\int_{ {{bottom}} }^{ {{top}} } {{integrand}} dx.</m></p></content>
         <outtro>
-            <!-- {{#converges}} -->
-            <p>Converges.</p>
-            <!-- {{/converges}} -->
-            <!-- {{^converges}} -->
-            <p>Diverges.</p>
-            <!-- {{/converges}} -->
+            <!-- {{#proper}} -->
+            <p>This integral is proper.</p>
+            <!-- {{/proper}} -->
+            <!-- {{^proper}} -->
+            <p><m>\renewcommand{\log}{\ln} \displaystyle\int_{ {{bottom}} }^{ {{top}} } {{integrand}} dx = {{int}}.</m></p>
+            <!-- {{/proper}} -->
         </outtro>
     </knowl>
     <!-- {{/tasks}} -->