MAT 101 MIDTERM COMPREHENSIVE
STUDY GUIDE 2026 FULL QUESTIONS AND
SOLUTIONS GRADED A+
◍ A function f(x) is odd if.
Answer: f(−x) = −f(x) for all x.
◍ A function f(x) is even if.
Answer: f(−x) = f(x) for all x.
◍ For any odd function, the integral from -a to a is:.
Answer: 0.
◍ Fundamental theorem of calculus.
Answer: ∫ f(x) dx on interval a to b = F(b) - F(a)where F is any
antiderivative of f.
◍ Indf. Integral of 1.
Answer: x+C
◍ Indf. Integral of x^n for (n DNE -1).
Answer: (x^(n+1))/(n+1) + C
◍ Indf. Integral of 1/x.
Answer: log(|x|) + C
◍ Indf. Integral of e^x.
Answer: e^x + C
◍ Indf. Integral of sin(x).
Answer: -cos(x) + C
◍ Indf. Integral of cos(x).
Answer: sin(x) + C
STUDY GUIDE 2026 FULL QUESTIONS AND
SOLUTIONS GRADED A+
◍ A function f(x) is odd if.
Answer: f(−x) = −f(x) for all x.
◍ A function f(x) is even if.
Answer: f(−x) = f(x) for all x.
◍ For any odd function, the integral from -a to a is:.
Answer: 0.
◍ Fundamental theorem of calculus.
Answer: ∫ f(x) dx on interval a to b = F(b) - F(a)where F is any
antiderivative of f.
◍ Indf. Integral of 1.
Answer: x+C
◍ Indf. Integral of x^n for (n DNE -1).
Answer: (x^(n+1))/(n+1) + C
◍ Indf. Integral of 1/x.
Answer: log(|x|) + C
◍ Indf. Integral of e^x.
Answer: e^x + C
◍ Indf. Integral of sin(x).
Answer: -cos(x) + C
◍ Indf. Integral of cos(x).
Answer: sin(x) + C
