MAT 266 Exam 1 (Ch 5.5, 6.1 - 6.5) Question and
answers correctly solved 2025/2026
1. Average Value of a
1/b-a (integral a to b) f(x)dx
Func- tion
2. Integration by parts
Integral of udv = uv - integral of vdu
for- mula
3. Trigonometric
asin(theta)
Substitu- tion for
root of a^2-x^2
asec(theta)
4. Trigonometric
Substitu- tion for
root of x^2-a^2 atan(theta)
5. Trigonometric
Substitu- tion for
root of a^2+x^2
6. sin^2x+cos^2x 1
7. sec^2x-tan^2x 1
8. sin^2x 1/2(1-cos2x)
9. cos^2x 1/2(1+cos2x)
Decom- position
10. Partial Fraction ax^2+bx+c
Decom- position
(ax+b)
11. Partial Fraction
Decom- position
(ax+b)^k
12. Partial Fraction
1/
3
answers correctly solved 2025/2026
1. Average Value of a
1/b-a (integral a to b) f(x)dx
Func- tion
2. Integration by parts
Integral of udv = uv - integral of vdu
for- mula
3. Trigonometric
asin(theta)
Substitu- tion for
root of a^2-x^2
asec(theta)
4. Trigonometric
Substitu- tion for
root of x^2-a^2 atan(theta)
5. Trigonometric
Substitu- tion for
root of a^2+x^2
6. sin^2x+cos^2x 1
7. sec^2x-tan^2x 1
8. sin^2x 1/2(1-cos2x)
9. cos^2x 1/2(1+cos2x)
Decom- position
10. Partial Fraction ax^2+bx+c
Decom- position
(ax+b)
11. Partial Fraction
Decom- position
(ax+b)^k
12. Partial Fraction
1/
3
