allery∫₀¹ x e^(x²) dx equals:
A(e-1)/2
Be/2
Ce
De²
Answer & Solution
Correct answer: A. (e-1)/2
Let u = x², du = 2x dx.
Integral becomes (1/2) ∫₀¹ e^u du = (1/2)[e^u]₀¹ = (1/2)(e - 1).
Keep practising Unit 6A: Indefinite Integrals & Fundamental Theorem
Browse all Unit 6A: Indefinite Integrals & Fundamental Theorem questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
The integrating factor of the linear differential equation $\dfrac{dy}{dx} + \dfrac{y}{x} The number of arbitrary constants in the general solution of a differential equation of orUsing the substitution $t = 1 + x^2$, $\displaystyle\int \dfrac{x}{1 + x^2}\,dx$ equals:$\displaystyle\int e^x\bigl(f(x) + f'(x)\bigr)\,dx$ equals:$\displaystyle\int \log x\,dx$ equals:$\displaystyle\int ec^2 x\,dx$ equals:$\displaystyle\int \dfrac{1}{ qrt{1 - x^2}}\,dx$ equals:$\displaystyle\int \dfrac{1}{1+x^2}\,dx$ equals: