The integral evaluates to [x^4/4 - x^3 + (3/2)x^2 - x] from 0 to 1 = 0.

∫_0^1 (x^4 - 2x^2 + 1) dx = [x^5/5 - (2/3)x^3 + x] from 0 to 1 = (1/5 - 2/3 + 1) = 1/15.

The integral evaluates to [x^5/5] from 0 to 1 = 1/5.

∫_0^π/2 cos^2(x) dx = π/4.

Using the identity sin^2(x) = (1 - cos(2x))/2, the integral evaluates to π/4.

The integral evaluates to [x^3 - 4x] from 1 to 2 = (8 - 8) - (1 - 4) = 3.

∫_1^2 (3x^2 - 4x + 1) dx = [x^3 - 2x^2 + x] from 1 to 2 = (8 - 8 + 2) - (1 - 2 + 1) = 1.

The integral evaluates to [x^2 + x] from 1 to 3 = (9 + 3) - (1 + 1) = 10.

sin^(-1)(0) = 0 and cos^(-1)(0) = π/2, thus the sum is 0 + π/2 = π/2.

sin^(-1)(1) = π/2 and cos^(-1)(0) = π/2. Therefore, π/2 + π/2 = π.

Faraday's law states that the induced EMF is proportional to the rate of change of magnetic flux.

'Thus' indicates a conclusion drawn from the previous statement.

'However' is the correct choice as it contrasts the expectation set by the first clause.

'Therefore' is the correct choice as it shows the result of his hard work.

The correct preposition is 'over'. The phrase is 'walked over the bridge'.

The correct preposition is 'on'. The phrase is 'jumped on the table'.

The correct conjunction is 'or'. It presents an alternative.

'So' indicates the consequence of being late.

'However' indicates a contrast to the initial desire.

'And' is appropriate here as it adds information about her love for travel.

'Thus' indicates a conclusion based on her tiredness.

'Unanimous' means that all members agreed, which fits the context of a decision made after debate.

'Therefore' indicates the result of overcoming the challenge.

a_10 = 3(10) + 2 = 30 + 2 = 32.

a_10 = 3(10^2) + 2(10) = 300 + 20 = 320.

The angle between the lines can be found using the formula tan(θ) = |(m1 - m2) / (1 + m1*m2)|, where m1 and m2 are the slopes of the lines. The slopes can be found from the equation.

The slopes are m1 = 2 and m2 = -0.5. The angle θ is given by tan(θ) = |(m1 - m2) / (1 + m1*m2)| = |(2 + 0.5) / (1 - 1)|, which is undefined, indicating 90 degrees.

The angle θ = cos⁻¹((u · v) / (|u| |v|)) = cos⁻¹(0) = 90 degrees.

cos(θ) = (A · B) / (|A| |B|). A · B = 1*2 + 2*0 + 2*2 = 6. |A| = √(1^2 + 2^2 + 2^2) = 3, |B| = √(2^2 + 0^2 + 2^2) = 2√2. cos(θ) = 6 / (3 * 2√2) = 1/√2, θ = 45°.

cos(θ) = (A · B) / (|A| |B|). A · B = 1*2 + 2*1 + 2*1 = 6; |A| = √(1^2 + 2^2 + 2^2) = 3; |B| = √(2^2 + 1^2 + 1^2) = √6. Thus, cos(θ) = 6 / (3√6) = 1/√6, θ = 45°.