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Find the value of the definite integral ∫_π/6 ^π/3( x+tan x) x dx .

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Wize University Calculus 1 Textbook > Integrals

Antiderivatives of Trig Functions

4 Activities

Wize University Calculus 1 Textbook > Integrals

Antiderivatives of Inverse Trig Functions

3 Activities

Find the value of the definite integral ∫π/6π/3(sec⁡x+tan⁡x)sec⁡xdx\displaystyle \int_{\pi/6 }^{\pi/3}(\sec x+\tan x)\sec x dx .
More Antiderivatives of Trig Functions Questions:
Derivatives/Antiderivatives
What is the derivative of f(x)=excos⁡xf(x)=e^{x}\cos x?
Derivatives/Antiderivatives
What is the derivative of f(x)=e2xcos⁡3xf(x)=e^{2x}\cos3x?
Indefinite Integrals with Trig and Inverse Trig
Find ∫(2x−34−x2+2sin⁡x)dx\displaystyle\int_{ }^{ }\left(2\sqrt{x}-\frac{3}{\sqrt{4-x^2}}+2\sin x\right)dx
Practice: Indefinite Integral
Find f(x)f\left(x\right), given that f′(x)=x2−2+sin⁡xf'\left(x\right)=x^2-2+\sin x and f(0)=3f\left(0\right)=3.
Practice: Indefinite Integral
Practice: Indefinite Integral
Find f(x)f\left(x\right), given that f′(x)=x2−2+sin⁡xf'\left(x\right)=x^2-2+\sin x and f(0)=3f\left(0\right)=3.
Indefinite Integrals with Trig and Inverse Trig
Find ∫(2x−34−x2+2sin⁡x)dx\displaystyle\int_{ }^{ }\left(2\sqrt{x}-\frac{3}{\sqrt{4-x^2}}+2\sin x\right)dx
Antiderivatives: Trigonometric Functions
Evaluate the integral∫[tan⁡2x+1+1sec⁡2x+sin⁡2x]dx\displaystyle \int_{ }^{ }\left[\tan^2x+1+\frac{1}{\sec^2x}+\sin^2x\right]dx.
Hint: First simplify using trig identities
Find the value of the definite integral ∫π/6π/3(sec⁡x+tan⁡x)sec⁡xdx\displaystyle \int_{\pi/6 }^{\pi/3}(\sec x+\tan x)\sec x dx .
Evaluate the indefinite integral ∫sec⁡θtan⁡θ−sin⁡(θ5)dθ\displaystyle \int\sec\theta\tan\theta-\sin\left(\frac{\theta}{5}\right)d\theta.
Evaluate the indefinite integral ∫sec⁡θtan⁡θ−sin⁡(θ5)dθ\displaystyle \int\sec\theta\tan\theta-\sin\left(\frac{\theta}{5}\right)d\theta.
Practice: Indefinite Integral (~F2018 Final Q26)
Practice: Indefinite Integral
Find f(x)f\left(x\right), given that f′(x)=x2−2+sin⁡xf'\left(x\right)=x^2-2+\sin x and f(0)=3f\left(0\right)=3.
Indefinite Integrals with Trig and Inverse Trig
Q:\textbf{Q:} Find ∫(2x−34−x2+2sin⁡x)dx\displaystyle\int_{ }^{ }\left(2\sqrt{x}-\frac{3}{\sqrt{4-x^2}}+2\sin x\right)dx
Antiderivatives: Indefinite with Trig
Find ∫(tan⁡2x+1sec⁡2x+1+xπ+sin⁡2x)dx\displaystyle\int_{ }^{ }\left(\tan^2x+\frac{1}{\sec^2x}+1+x^\pi+\sin^2x\right)dx
Antiderivatives: Product with Trig
Find dfdθ\displaystyle\frac{df}{d\theta} given f(θ)=(sin⁡θ−cos⁡θ)sec⁡θ\displaystyle f(\theta)=(\sin\theta-\cos\theta)\sec\theta
Practice: Indefinite Integral
Evaluate the integral∫[tan⁡2x+1+1sec⁡2x+sin⁡2x]dx\displaystyle \int_{ }^{ }\left[\tan^2x+1+\frac{1}{\sec^2x}+\sin^2x\right]dx.
Hint: First simplify using trig identities
Practice: Indefinite Integral
Evaluate the integral∫[tan⁡2x+1+1sec⁡2x+sin⁡2x]dx\displaystyle \int_{ }^{ }\left[\tan^2x+1+\frac{1}{\sec^2x}+\sin^2x\right]dx.
Hint: First simplify using trig identities
Find ∫0π∣cos⁡ x∣dx\displaystyle\int_0^{\pi}\left|\cos\ x\right|dx
Antiderivatives: Trigonometric Functions
Find
∫1+sin⁡3xsin⁡2xdx\int \frac{1+\sin^3 x}{\sin^2 x} dx
Find an antiderivative for
f(x)=−cos⁡x+x2f(x)=-\cos{x}+x^2
Antiderivatives: Trigonometric Functions
Find the definite integral ∫π/6π/3(sec⁡x+tan⁡x)sec⁡xdx\int_{\pi/6 }^{\pi/3}(\sec x+\tan x)\sec x dx
final114
Find the indefinite integral ∫(1x2+sin⁡x)dx\displaystyle\int\bigg(\frac{1}{x^2}+\sin x\bigg)dx
Antiderivatives: Trigonometric Functions
Evaluate the integral∫[tan⁡2x+1+1sec⁡2x+sin⁡2x]dx\displaystyle \int_{ }^{ }\left[\tan^2x+1+\frac{1}{\sec^2x}+\sin^2x\right]dx.
Hint: First simplify using trig identities
final114
Find the definite integral ∫π/6π/3(sec⁡x+tan⁡x)sec⁡xdx\int_{\pi/6 }^{\pi/3}(\sec x+\tan x)\sec x dx
Find the exact value of
∫0πsin⁡xdx\int_0^{\pi}\sin xdx
Antiderivatives: Product with Trig
Find dfdθ\displaystyle\frac{df}{d\theta} given f(θ)=(sin⁡θ−cos⁡θ)sec⁡θ\displaystyle f(\theta)=(\sin\theta-\cos\theta)\sec\theta
Find the indefinite integral ∫(1x2+sin⁡x)dx\displaystyle\int\bigg(\frac{1}{x^2}+\sin x\bigg)dx . Use C for the integration constant.
Antiderivatives: Indefinite with Trig
Find ∫(tan⁡2x+1sec⁡2x+1+xπ+sin⁡2x)dx\displaystyle\int_{ }^{ }\left(\tan^2x+\frac{1}{\sec^2x}+1+x^\pi+\sin^2x\right)dx
Indefinite Integrals with Trig and Inverse Trig
Find ∫(2x−34−x2+2sin⁡x)dx\displaystyle\int_{ }^{ }\left(2\sqrt{x}-\frac{3}{\sqrt{4-x^2}}+2\sin x\right)dx
Derivatives/Antiderivatives
Compute the second derivative of f(x)=etan⁡xf(x)=e^{\tan x}.
Evaluate the indefinite integral ∫sec⁡θtan⁡θ−sin⁡(θ5)dθ\displaystyle \int\sec\theta\tan\theta-\sin\left(\frac{\theta}{5}\right)d\theta.
Find ∫0π∣cos⁡ x∣dx\displaystyle\int_0^{\pi}\left|\cos\ x\right|dx
Antiderivatives: Trigonometric Functions
Evaluate ∫π3π∣cos⁡x∣dx\int_{\frac{\pi}{3}}^{\pi}\left|\cos x\right|dx.
Antiderivatives: Trigonometric and Exponential Functions
If f′′(x)=cos⁡(2x)−x4+exf''\left(x\right)=\cos\left(2x\right)-x^4+e^x, f(0)=0=f′(0)f\left(0\right)=0=f'\left(0\right)
Practice: Indefinite Integral
Practice: Indefinite Integral
Find f(x)f\left(x\right), given that f′(x)=x2−2+sin⁡xf'\left(x\right)=x^2-2+\sin x and f(0)=3f\left(0\right)=3.
For each of the following functions, find the most general antiderivative.
f(x)=−cos⁡x+x2f(x)=-\cos{x}+x^2
Find the most general antiderivative.
f(x)=−cos⁡x+x2f(x)=-\cos{x}+x^2
More Antiderivatives of Inverse Trig Functions Questions:
Integration Medley
Practice Question
Evaluate ∫x4+1x2+1  ⁣dx{\displaystyle\int} \frac{x^4+1}{x^2+1}\de{x}.
Evaluate the integral ∫x4+1x2+1dx\displaystyle\int\frac{x^4+1}{x^2+1}dx.
Find the value of the definite integral ∫π/6π/3(sec⁡x+tan⁡x)sec⁡xdx\displaystyle \int_{\pi/6 }^{\pi/3}(\sec x+\tan x)\sec x dx .
Evaluate the indefinite integral ∫6x+e−6x−3x2+1dx\displaystyle \int6^x+e^{-6x}-\frac{3}{x^2+1}dx.
Evaluate the indefinite integral ∫6x+e−6x−3x2+1dx\displaystyle \int6^x+e^{-6x}-\frac{3}{x^2+1}dx.
Practice: Definite Integral (~F2017 Final Q26)
Practice: Definite Integral
Evaluate ∫0319+x2+2xln⁡2 dx\int_0^3\frac{1}{9+x^2}+2^x\ln2\ dx.
Integration Medley
Practice Question
Evaluate ∫x4+1x2+1  ⁣dx{\displaystyle\int} \frac{x^4+1}{x^2+1}\de{x}.
Integration Medley
Practice Question
Evaluate ∫x4+1x2+1  ⁣dx{\displaystyle\int} \frac{x^4+1}{x^2+1}\de{x}.
Integration Medley
Practice Question
Evaluate ∫x4+1x2+1  ⁣dx{\displaystyle\int} \frac{x^4+1}{x^2+1}\de{x}.
Evaluate ∫−10dx1−x2\int_{-1}^0\frac{dx}{\sqrt{1-x^2}}
Integration Medley
Practice Question
Evaluate ∫x4+1x2+1  ⁣dx{\displaystyle\int} \frac{x^4+1}{x^2+1}\de{x}.
Practice: Definite Integral
Evaluate ∫0319+x2+2xln⁡2 dx\displaystyle \int_0^3\frac{1}{9+x^2}+2^x\ln2\ dx.
Antiderivatives: Inverse Trigonometric Functions
Evaluate dducos⁡−1usin⁡−1u\displaystyle \frac{\text{d}}{\text{d}u} \frac{\cos^{-1}u}{\sin^{-1}u}. It is not necessary to simplify.
Evaluate the integral ∫x4+1x2+1dx\displaystyle\int\frac{x^4+1}{x^2+1}dx.
Find the indefinite integral ∫(11+x+11+x2)dx\int(\frac{1}{1+x}+\frac{1}{1+x^2})dx.
Evaluate the indefinite integral ∫6x+e−6x−3x2+1dx\displaystyle \int6^x+e^{-6x}-\frac{3}{x^2+1}dx.
Evaluate ∫−10dx1−x2\int_{-1}^0\frac{dx}{\sqrt{1-x^2}}
Antiderivatives: Inverse Trigonometric Functions
Find ∫24−t2dt\int_{ }^{ }\frac{2}{\sqrt{4-t^2}}dt.
Practice: Definite Integral
Practice: Definite Integral
Evaluate ∫0319+x2+2xln⁡2 dx\int_0^3\frac{1}{9+x^2}+2^x\ln2\ dx.