Postgraduate Mathematics III task 20: Evaluate ∫₀^5 (4x+4) dx.
An antiderivative is 4/2 x²+4x. At x=5, the value is 70.0.
Practice China questions with answers and explanations.
An antiderivative is 4/2 x²+4x. At x=5, the value is 70.0.
The dot product is 4×2+5×4=28.
Rewrite the value using base 5: 3125 = 5^5. Matching exponents gives x = 5.
Choose an option to check your answer.
Use the circle-area formula A = πr². Substituting r = 9 gives A = π × 9² = 81π.
Percentage=(8/23)×100=34.78.
Subtract 4 from both sides and divide by 3: x = (34-4)/3 = 10.
By Vieta’s formula, the sum of the roots equals the coefficient 7.
Percentage=(7/22)×100=31.82.
Subtract 3 from both sides and divide by 2: x = (21-3)/2 = 9.
By Vieta’s formula, the sum of the roots equals the coefficient 12.
aₙ=a₁+(n−1)d=2+(8−1)×4=30.
Choose an option to check your answer.
The sum is n(n+1)/2=10, so the mean is 10/4.