Question

Please

clearly show the answer of each box

If ∫₀π / 299 cos t/√(1+sin ² t) d t=∫ₐ ᵇ q θ d θ
then a=__

Answer 1

To solve the given integral equation, we need to find the values of a and b. By evaluating the integrals on both sides and setting them equal to each other, we can determine the values of a and b.

Step-by-step explanation:

To solve the integral equation ∫₀π / 299 cos t/√(1+sin ² t) d t=∫ₐ ᵇ q θ d θ, we need to find the values of a and b. Let's first evaluate the integral on the left side of the equation. Using the identity cos²(t) = (1+cos(2t))/2, we have:

1. ∫₀π / 299 cos t/√(1+sin ² t) d t = ∫₀π / 299 cos t/√(1+(1-cos²(t))) d t
2. Using the substitution u = sin(t), we can rewrite the integral as:
3. ∫₀π / 299 cos t/√(1-u²) d t = ∫₀π / 299 du/√(1-u²)

Now, let's solve the integral on the right side of the equation

∫ₐ ᵇ q θ d θ = q(θ) |ₐ ᵇ = q(b) - q(a)

By setting the integrals on both sides of the equation equal to each other, we can find the values of a and b.